Question 13 Marks
Find the difference:
$\frac3{1}{5}-\frac{7}{10}=\frac{16\times2}{5\times2}=\frac{32}{10}$
Answer$\frac3{1}{5}-\frac{7}{10}=\frac{16\times2}{5\times2}=\frac{32}{10}$
LCM of 5 and 10 = 10
$\therefore\frac{16}{5}=\frac{16\times2}{5\times2}=\frac{32}{10}$
$\frac{16}{5}-\frac{7}{10}=\frac{32}{10}-\frac{7}{10}=\frac{32-7}{10}$
$\frac{25}{10}=\frac{25\div5}{10\div5}=\frac{5}{2}=2\frac{1}{2}$
View full question & answer→Question 23 Marks
A car covers a certain distance at a uniform speed of $66\frac{2}{3}\text{km/h}$ How much distance will it cover in 9 hours?
View full question & answer→Question 33 Marks
Vikas can cover a distance of $20\frac{2}{3}\text{km.}$ in $7\frac{3}{4}\text{hours}$ hours on foot. How many km per hour does he walk?
AnswerDistance covered in $7\frac{3}{4}\text{hours}=20\frac{2}{3}\text{km}$$\therefore$ Distance covered in one hour
$=20\frac{2}{3}\div7\frac{3}{4}$
$=\Big(\frac{62}{3}\div\frac{31}{4}\Big)\text{km}$
$=\frac{62}{3}\times\frac{4}{31}=\frac{2\times4}{3}\text{km}$
$=\frac{8}{3}\text{km}= 2\frac{2}{3}\text{km}$
View full question & answer→Question 43 Marks
Apples are sold at $\text{Rs. }48\frac{4}{5}\text{/kg}$ What is the cost of $3\frac{3}{4}\text{kg}$ of apples?
AnswerPrice of 1kg of apple $\text{Rs. }48\frac{4}{5}=\text{Rs. }\frac{244}{5}$
$\therefore$ Price of $3\frac{3}{4}\text{kg}$ of apples $\text{Rs. }\frac{244}{5}\times3\frac{3}{4}$
$=\text{Rs. }\Big(\frac{244}{5}\times\frac{15}{4}\Big)$
$=\text{Rs. }(61\times3)=\text{Rs. }183$
View full question & answer→Question 53 Marks
Reenu got $\frac{2}{7}$ part of an apple while Sonal got $\frac{4}{5}$ part of it. Who got the larger part and by how much?
AnswerReenu get $\frac{2}{7}$ of an apple while sonal gets $\frac{2}{7}$ part of it
Now $\frac{2}{7},\frac{4}{5}$
$\Rightarrow2\times5,4\times7$
$\Rightarrow10,28$
$\therefore$ 28 is greater
$\therefore\frac{4}{5}$ part is greater
Difference $=\frac{4}{5}-\frac{2}{7}$
$=\frac{4\times7-2\times5}{35}$
$=\frac{28-10}{35}=\frac{18}{35}$
$\therefore$ Sonal gets greater part and by $\frac{18}{35}$ part
View full question & answer→Question 63 Marks
Simplify:
$8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}=\frac{53}{6}-\frac{27}{8}+\frac{19}{12}$
Answer$8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}=\frac{53}{6}-\frac{27}{8}+\frac{19}{12}$
LCM of 6, 8, 12 = 24
$\therefore\frac{53}{6}=\frac{53\times4}{6\times4}=\frac{212}{24}$
$\frac{27}{8}=\frac{27\times3}{6\times4}=\frac{81}{24}$
$\frac{19}{12}=\frac{19\times2}{12\times2}=\frac{38}{24}$
$\therefore\frac{53}{6}-\frac{27}{8}+\frac{19}{12}$
$=\frac{212}{24}-\frac{81}{24}+\frac{38}{24}$
$=\frac{169}{24}=7\frac{1}{24}$
View full question & answer→Question 73 Marks
Arrange the following fractions in descending order:
$\frac{2}{5},\frac{3}{5},\frac{7}{10},\frac{8}{15}$
Answer$\frac{2}{5},\frac{3}{5},\frac{7}{10},\frac{8}{15}$
Writing them into like fractions, LCM of 2, 5, 10, 15 = 30
$\therefore\frac{2}{3}=\frac{2\times10}{3\times10}=\frac{20}{30}$
$\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}$
$\frac{7}{10}=\frac{7\times3}{10\times3}=\frac{21}{30}$
$\frac{8}{15}=\frac{8\times2}{15\times2}=\frac{16}{30}$
$\frac{21}{30}>\frac{20}{30}>\frac{18}{30}>\frac{16}{30}$
or $\frac{7}{10}>\frac{2}{5}>\frac{3}{5}>\frac{8}{15}$
View full question & answer→Question 83 Marks
There are 42 students in a class and $\frac{5}{7}$ of the students are boys. How many girls are there in the class?
AnswerTotal number of students in a class = 42
Number of boys $=\frac{5}{7}\text{ of }42=5\times6=30$
Number of girls = 42 - 30 = 12
View full question & answer→Question 93 Marks
Find the sum:
$\frac{5}{6}+\frac{7}{8}$
Answer$\frac{5}{6}+\frac{7}{8}$
LCM of 6, and 8 = 24
$\therefore\frac{5}{6}=\frac{5\times4}{6\times4}=\frac{20}{24}$
$\frac{7}{8}=\frac{7\times3}{8\times3}=\frac{21}{24}$
$\therefore\frac{5}{6}+\frac{7}{8}=\frac{20}{24}=\frac{21}{24}$
$=\frac{20+21}{24}=\frac{41}{24}=1\frac{17}{24}$
View full question & answer→Question 103 Marks
AnswerTotal duration of the film $=3\frac{2}{3}=\frac{11}{3}$ hours.
Time spent on advertisement $=1\frac{1}{2}=\frac{3}{2}$ hours.
$\therefore$ Actual duration of the film $=\frac{11}{3}-\frac{3}{2}$
$=\frac{13}{6}=2\frac{1}{6}$ hours.
View full question & answer→Question 113 Marks
By what number should $6\frac{2}{9}$ be divided to obtain $4\frac{2}{3}?$
AnswerRequired number $=6\frac{2}{9}\div4\frac{2}{3}$
$=\frac{56}{9}\div\frac{14}{3}$
$=\frac{56}{9}\div\frac{3}{14}$
$\Big[\because\text{ Reciprocal of }\frac{14}{3}=\frac{3}{14}\Big]$
$=\frac{4}{3}=1\frac{1}{3}$
Hence, we have to divide $6\frac{2}{9}\text{ by}$
$1\frac{1}{3}$ to abtain $4\frac{2}{3}$
View full question & answer→Question 123 Marks
Mangoes are sold at $\text{Rs. }43\frac{1}{2}\text{per kg.}$ What is the weight of mangoes available for $\text{Rs. }326\frac{1}{4}?$
AnswerPrice of one kg. of mangoes $=\text{Rs. }43\frac{1}{2}$
$=\text{Rs. }\frac{87}{2}$
Total amount $=\text{Rs. }326\frac{1}{4}=\text{Rs. }\frac{1305}{4}$
$\therefore$ Quantity of mangoes sold
$=\text{Rs. }\frac{1305}{4}\div\text{Rs. }\frac{87}{2} $
$=\frac{1305}{4}\times\frac{2}{87}=\frac{15}{2}\text{kg.}$
$=7\frac{1}{2}\text{kg.}$
View full question & answer→Question 133 Marks
Simplify:
$\frac{2}{3}+\frac{5}{6}-\frac{1}{9}$
Answer$\frac{2}{3}+\frac{5}{6}-\frac{1}{9}$
LCM of 3, 6, 9 = 18
$\therefore\frac{2}{3}=\frac{2\times6}{3\times6}=\frac{12}{18}$
$\frac{1}{9}=\frac{1\times2}{9\times2}=\frac{2}{18}$
$\therefore\frac{12+15-12}{18}=\frac{27-2}{18}$
$=\frac{25}{18}=1\frac{7}{18}$
View full question & answer→Question 143 Marks
Find the sum:
$\frac{8}{9}+\frac{7}{12}$
Answer$\frac{8}{9}+\frac{7}{12}$
LCM of 9 and 12 = 36
$\therefore\frac{8}{9}=\frac{8\times4}{9\times4}=\frac{32}{36}$
$\frac{7}{12}=\frac{7\times3}{12\times3}=\frac{21}{36}$
$\therefore\frac{8}{9}+\frac{7}{12}=\frac{32}{36}=\frac{21}{36}$
$=\frac{32+21}{36}=\frac{53}{36}=1\frac{17}{36}$
View full question & answer→Question 153 Marks
Find the sum:
$8\frac{3}{4}+10\frac{2}{5}$
Answer$8\frac{3}{4}+10\frac{2}{5}$
$=\frac{35}{4}+\frac{52}{5}$
LCM of 4 and 5 = 20
$\therefore\frac{35}{4}=\frac{35\times5}{4\times5}=\frac{175}{20}$
$\frac{52}{5}=\frac{52\times4}{5\times4}=\frac{208}{20}$
$\therefore\frac{35}{4}+\frac{52}{5}+\frac{175}{20}+\frac{208}{20}$
$=\frac{175+208}{20}=\frac{383}{20}=19\frac{3}{20}$
View full question & answer→Question 163 Marks
Aneeta bought $3\frac{3}{4}\text{kg}$ apples and $4\frac{1}{2}\text{kg}$ guava. What is the total weight of fruits purchased by her?
AnswerAneeta bought apples $3\frac{3}{4}\text{kg}=\frac{15}{4}\text{kg}$
and gauva $=4\frac{1}{2}\text{kg}=\frac{9}{2}\text{kg}$
$\therefore$ Total weight of fruits $=\frac{15}{4}+\frac{9}{2}$
$=\frac{15+18}{4}=\frac{33}{4}\text{kg}$
$=8\frac{1}{4}\text{kg}$
View full question & answer→Question 173 Marks
Find the difference:
$2\frac{5}{9}-1\frac{7}{15}=\frac{23}{9}-\frac{22}{15}$
Answer$2\frac{5}{9}-1\frac{7}{15}=\frac{23}{9}-\frac{22}{15}$LCM of 9 and 15= 45
$\therefore\frac{23}{9}\frac{23\times5}{9\times5}=\frac{115}{45}$
$\frac{22}{15}=\frac{22\times3}{15\times3}=\frac{66}{45}$
$\therefore\frac{23}{9}-\frac{22}{15}=\frac{115}{45}-\frac{66}{45}$
$=\frac{115-66}{45}=\frac{49}{45}$
View full question & answer→Question 183 Marks
Milk is sold at $\text{Rs. }37\frac{3}{4}\text{/litre}.$ Find the cost of $6\frac{2}{5}\text{ litres}$ of milk.
AnswerCost of 1 litres of milk $=\text{Rs. }37\frac{3}{4}$
$=\text{Rs. }\frac{151}{4}$
Cost of $6\frac{2}{5}\text{ litres}$ of milk $=\text{Rs. }\Big(\frac{151}{4}\times6\frac{2}{5}\Big)$
$=\text{Rs. }\Big(\frac{151}{4}\times\frac{32}{5}\Big)$
$=\text{Rs. }\Big(\frac{151\times48}{1\times5}\Big)=\text{Rs. }\frac{1208}{5}$
$=\text{Rs. }241\frac{3}{5}$
Hence, the cost of $6\frac{2}{5}\text{ litres}$ of milk is $=\text{Rs. }241\frac{3}{5}$
View full question & answer→Question 193 Marks
Simplify:$1\frac{3}{4}\times2\frac{2}{5}\times3\frac{4}{7}$
AnswerWe have,
$1\frac{3}{4}\times2\frac{2}{5}\times3\frac{4}{7}$
$=\frac{7}{4}\times\frac{12}{5}\times\frac{25}{7}$
$=\frac{7\times12\times25}{4\times5\times7}$
$=\frac{1\times3\times5}{1\times1\times1}=15$
View full question & answer→Question 203 Marks
If the cost of a notebook is $\text{Rs. }27\frac{3}{4},$ how many notebooks can be purchased for $\text{Rs. }326\frac{1}{4}?$
AnswerCost of one notebook $=\text{Rs. }27\frac{3}{4}=\text{Rs. }\frac{111}{4}$Total amount $=\text{Rs. }249\frac{3}{4}=\text{Rs. }\frac{999}{4}$
$\therefore$ Number of notebook can be purchased,
$=\frac{999}{4}\div\frac{111}{4}$
$=\frac{999}{4}\times\frac{111}{4}=9$
View full question & answer→Question 213 Marks
A group of students arranged a picnic. Each student contributed $\text{Rs. }261\frac{1}{2}.$ The total contribution was $\text{Rs. }2876\frac{1}{2}.$ How many students are there in the group?
AnswerContribution by each student $=\text{Rs. }261\frac{1}{2}$ $=\text{Rs. }\frac{523}{2}$ Total contribution collected $=\text{Rs. }28761\frac{1}{2}$ $=\text{Rs. }\frac{5753}{2}$ $\therefore$ Number of students $=\text{Rs. }\frac{5753}{2}\div\frac{523}{2}$$=\frac{5753}{2}\times\frac{2}{523}=11$
View full question & answer→Question 223 Marks
The product of two numbers is $15\frac{5}{6}.$ If one of the numbers is $6\frac{1}{3},$find the other.
Answerproduct of two numbers $=15\frac{5}{6}=\frac{95}{6}$
One number $=6\frac{1}{3}=\frac{19}{3}$
$\therefore$ Second number $=\frac{95}{6}=\frac{19}{3}$
$=\frac{95}{6}=\frac{3}{19}=\frac{5\times1}{2\times1}=\frac{5}{2}$
$=2\frac{1}{2}$
View full question & answer→Question 233 Marks
Simplify:
$8-4\frac{1}{2}-2\frac{4}{1}=\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$
Answer$8-4\frac{1}{2}-2\frac{4}{1}=\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$LCM of 1, 2, 4 = 4
$\therefore\frac{8}{1}=\frac{8\times4}{1\times4}=\frac{32}{4}$
$\frac{9}{2}=\frac{9\times2}{2\times2}=\frac{18}{4}$
$\frac{9}{4}=\frac{9}{4}$
$\therefore\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$
$=\frac{32}{4}-\frac{18}{4}-\frac{9}{4}$
$=\frac{32-27}{4}=\frac{5}{4}=1\frac{1}{4}$
View full question & answer→Question 243 Marks
By what number should $9\frac{4}{5}$be multiplied to get 42?
Answerproduct of two numbers = 42
One number $=9\frac{4}{5}=\frac{49}{5}$
$\therefore$ Second number $=42\div\frac{49}{5}=42\times\frac{5}{49}$
$=\frac{6\times5}{7}=\frac{30}{7}=4\frac{2}{7}$
View full question & answer→Question 253 Marks
Find the area of a rectangular park which is $41\frac{2}{3}\text{m}$ long and 18
AnswerLength of rectangular field (l)
$=41\frac{2}{3}\text{m}=\frac{125}{3}\text{m}$
Breadth (b) $=18\frac{3}{5}\text{m}=\frac{93}{5}\text{m}$
$\therefore$ Area = l × b
$=\frac{125}{3}\times\frac{93}{5}\text{m}^2$
$=25\times31\text{m}^{2}=775\text{m}^2$
View full question & answer→Question 263 Marks
What should be added to $6\frac{3}{5}$ to get 15?
AnswerRequired number to be added
$=15-6\frac{3}{5}$
$=\frac{15}{6}-\frac{33}{5}$
$=\frac{75-33}{5}$ [$\because$ LCM 1 and 5 = 5 ]
$=\frac{42}{5}=8\frac{2}{5}$
Hence, the required number is $8\frac{2}{5}$
View full question & answer→Question 273 Marks
Arrange the following fractions in descending order:
$\frac{3}{4},\frac{7}{8},\frac{7}{12},\frac{17}{24}$
Answer$\frac{3}{4},\frac{7}{8},\frac{7}{12},\frac{17}{24}$
Writing them into like fractions, LCM of 4, 8, 12, and 24
$\therefore\frac{3}{4}=\frac{3\times6}{4\times6}=\frac{18}{24}$
$\frac{7}{8}=\frac{7\times3}{8\times3}=\frac{21}{24}$
$\frac{7}{12}=\frac{7\times2}{12\times2}=\frac{14}{24}$
$\frac{17}{14}=\frac{17}{14}$
Now, arranging them in descending order,
$\frac{21}{24}>\frac{18}{24}>\frac{17}{24}>\frac{14}{24}$
or $\frac{7}{8}>\frac{3}{4}>\frac{17}{24}>\frac{7}{12}$
View full question & answer→Question 283 Marks
Each side of a square field is $4\frac{2}{3}\text{m.}$ Find its area.
AnswerLength of each side of a square
$=4\frac{2}{3}\text{m}=\frac{14}{3}\text{m}$
$\therefore$ Area = side × side $=\frac{14}{3}\times\frac{14}{3}$ square metres
$=\frac{196}{9}=21\frac{7}{9}$square metres.
View full question & answer→Question 293 Marks
Of $\frac{2}{3}$ and $\frac{5}{9},$which is greater and by how much?
Answer$\frac{2}{3}\text{ and }\frac{5}{9}$
LCM of 3 and 9 = 9
$\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}$
$\therefore\frac{2}{3}$ is greater than $\frac{5}{9}$
or $\frac{2}{3}$ is greater than $\frac{5}{9}$
and $\frac{6}{9}-\frac{5}{9}=\frac{1}{9}$
$\therefore\frac{2}{3}$ is greater than $\frac{5}{9}\text{ by }\frac{1}{9}$
View full question & answer→Question 303 Marks
Each side of a square is $5\frac{2}{3}\text{m}$ long. Find its area.
AnswerSide of the square $=5\frac{2}{3} =\frac{17}{3}\text{m}$
Its area $=(\text{side})^2=\Big(\frac{17}{3}\text{m}\Big)$
$=\Big(\frac{17}{3}\text{m}\times\frac{17}{3}\text{m}\Big)$
$=\Big(\frac{289}{9}\Big)\text{m}^2=35\frac{1}{9}\text{m}^2$
Hence, the area of the square is $32\frac{1}{9}\text{m}^2$
View full question & answer→Question 313 Marks
At a charity show the price of each ticket was $\text{Rs. }33\frac{1}{2}.$ The total amount collected by a boy was $\text{Rs. }877\frac{1}{2}.$ How many tickets were sold by him?
AnswerPrice of one ticket $=\text{Rs. }32\frac{1}{2}=\text{Rs. }\frac{65}{2}$Total amount collected $=\text{Rs. }877\frac{1}{2}$
$=\text{Rs. }\frac{1755}{2}$
$\therefore$ Number of ticket sold $=\text{Rs. }\frac{1755}{2}\div\frac{65}{2}$
$=\frac{1755}{2}\times\frac{2}{65}=27$
View full question & answer→Question 323 Marks
By what number should $6\frac{2}{9}$be divided to gobtain $4\frac{2}{3}?$
Answerproduct of two numbers $6\frac{2}{9}=\frac{56}{9}$
One number $=4\frac{2}{3}=\frac{14}{3}$
$\therefore$ Required number $\frac{56}{9}\div\frac{14}{3}$
$=\frac{56}{9}\times\frac{3}{14}=\frac{4\times1}{3\times1}=\frac{4}{3}=1\frac{1}{3}$
View full question & answer→Question 333 Marks
A bucket contains $20\frac{1}{2}\text{litre}$ of water. A small jug has a capacity of $\frac{3}{4}\text{litre}.$ How many times the jug has to be filled with water from the bucket to get it emptied?
AnswerQuantity of water in a bucket
$=20\frac{1}{4}\text{l}=\frac{81}{4}\text{l}$
Quantity of water in a jug $=\frac{3}{4}\text{l}$
$\therefore$ Number of jug which to be filled,
$=\frac{81}{4}\text{l}\div\frac{3}{4}\text{l}$
$=\frac{81}{4}\times=\frac{4}{3}=27$
View full question & answer→Question 343 Marks
Arrange the following fractions in ascending order:
$\frac{3}{4},\frac{7}{8},\frac{7}{12},\frac{17}{24}$
Answer$\frac{3}{4},\frac{7}{8},\frac{7}{12},\frac{17}{24}$Writing them into like fractions, LCM of 4, 6, 9 and 12 = 36
$\therefore\frac{3}{4}=\frac{3\times9}{4\times9}=\frac{27}{36}$ $\frac{5}{6}=\frac{5\times6}{6\times6}=\frac{30}{36}$ $\frac{7}{9}=\frac{7\times4}{9\times4}=\frac{28}{36}$ $\frac{11}{12}=\frac{11\times3}{12\times3}=\frac{33}{36}$Now, arranging them in ascending order,
$\frac{27}{36}<\frac{28}{36}<\frac{30}{36}<\frac{33}{36}$or $\frac{3}{4}<\frac{7}{9}<\frac{5}{6}<\frac{11}{12}$
View full question & answer→Question 353 Marks
Find the sum:
$3\frac{4}{5}+2\frac{13}{10}+1\frac{1}{15}$
Answer$3\frac{4}{5}+2\frac{13}{10}+1\frac{1}{15}$
$=\frac{19}{5}+\frac{23}{10}+\frac{16}{15}$
LCM of 5, 10, 15 = 30
$\therefore\frac{19}{5}=\frac{15\times6}{5\times6}=\frac{114}{30}$
$\frac{23}{10}=\frac{23\times3}{10\times3}=\frac{69}{30}$
$\frac{16}{15}=\frac{16\times2}{15\times2}=\frac{32}{30}$
$\therefore=\frac{19}{5}+\frac{23}{10}+\frac{16}{15}$
$=\frac{114}{30}+\frac{69}{30}+\frac{32}{30}$
$=\frac{114+69+32}{30}=\frac{215}{30}$
$=\frac{215\div5}{30\div5}=\dfrac{43}{6}7\frac{1}{6}$
View full question & answer→Question 363 Marks
The cost of a pen is $\text{Rs. }16\frac{3}{5}$and that of a pencil is $\text{Rs. }4\frac{3}{4}$ Which costs more and by how much?
AnswerCost of the pen $=\text{Rs. }16\frac{3}{5} =\text{Rs. }\frac{83}{5}$
Cost of the pencil $=\text{Rs. }4\frac{3}{4} =\text{Rs. }\frac{19}{4}$
Now, LCM of 5 and 4 = 20
$\therefore\frac{83}{5}=\frac{83\times4}{5\times4}=\frac{332}{20}$
$\frac{19}{4}=\frac{19\times5}{5\times4}=\frac{95}{20}$
It is clear that cost of pen is more than that of a pencil
$\therefore\frac{332}{20}-\frac{95}{20}=\frac{237}{20}=\text{Rs. }11\frac{17}{20}$
$\therefore$ The cost of pen is more than pencils by
$=\text{Rs. }11\frac{17}{20}$
View full question & answer→Question 373 Marks
For a particular show in a circus, each ticket costs $\text{Rs. }35\frac{1}{2}$ If 308 tickets are sold for the show, how much amount has been collected?
AnswerOne ticket costs $=\text{Rs. }35\frac{1}{2}$
$=\text{Rs. }\frac{71}{2}$
$\therefore$ 308 tickets will cost $=\text{Rs. }\frac{71}{2}\times308$
$=\text{Rs. }(71\times154)$
$=\text{Rs. }10934$
View full question & answer→Question 383 Marks
Find the difference:
$7-4\frac{2}{3}=\frac{7}{1}-\frac{14}{3}$
Answer$3\frac{3}{10}-1\frac{7}{15}=\frac{33}{10}-\frac{22}{15}$
LCM of 1 and 15 = 30
$\therefore\frac{33}{10}\frac{33\times3}{10\times3}=\frac{99}{30}$
$\frac{22}{15}=\frac{22\times2}{15\times2}=\frac{44}{30}$
$=\frac{21-14}{3}=-\frac{7}{3}=2\frac{1}{3}$
$\therefore\frac{33}{10}-\frac{22}{15}=\frac{99}{30}-\frac{44}{30}$
$=\frac{99-44}{30}=\frac{55}{30}=1\frac{5}{6}$
View full question & answer→Question 393 Marks
Simplify:
$9\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}$
AnswerWe have,
$9\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}$
$\frac{59}{6}-\frac{35}{8}+\frac{31}{12}$
$\frac{236-105+62}{24}$ [$\because$ LCM of 6, 8 and 12 = 24]
$=\frac{298-105}{24}=\frac{193}{24}$
$=8\frac{1}{24}$
View full question & answer→Question 403 Marks
Preeti bought $8\frac{1}{2}\text{kg}$ of sugar for $\text{Rs. }242\frac{1}{4}.$ Find the price of sugar per kg.
AnswerPrice of $8\frac{1}{2}\text{kg}$ of sugar $=\text{Rs. }242\frac{1}{4}$$\therefore$ Price of one kg $=\text{Rs. }242\frac{1}{4}\div8\frac{1}{2}$
$=\text{Rs.}\Big(\frac{969}{4}\div\frac{17}{2}\Big)$
$=\text{Rs. }\frac{969}{4}\times\frac{2}{17}=\text{Rs.}\frac{57\times1}{2\times1}$
$=\text{Rs. }\frac{57}{2}=\text{Rs. }28\frac{1}{2}$
View full question & answer→Question 413 Marks
A rope of length $13\frac{1}{2}\text{m.}$ has been divided into 9 pieces of the same length. What is the length of each piece?
AnswerTotal length of the rope $=13\frac{1}{2}=\frac{27}{2}\text{m}$
Number od pieces = 9
$\therefore$ Length of each piece $=\frac{27}{2}\div9=\frac{27}{2}\times\frac{1}{9}$
$=\frac{3\times1}{2\times1}=\frac{3}{2}=1\frac{1}{2}\text{m}$
View full question & answer→Question 423 Marks
By selling oranges at the rate of $\text{Rs. }6\frac{3}{4}$ per orange, a man gets Rs. 378. How many oranges does he sell?
AnswerTotal amount of oranges $=\text{Rs. }378$
and price of one orange $=\text{Rs. }6\frac{3}{4}$
$\therefore$ Total number of oranges,
$= \text{Rs. } 378\div \text{Rs. }6\frac{3}{4}$
$=378\div\frac{27}{4}$
$=378\times\frac{4}{27}=14\times4$
$=56$
View full question & answer→Question 433 Marks
Nine boards are stacked on the top of each other. The thickness of each board is $3\frac{2}{3}\text{cm}$. How high is the stack?
AnswerThickness of one board $3\frac{2}{3}\text{cm}=\frac{11}{3}\text{cm}$
$\therefore$ Thickness of 9 boards $=\frac{11}{3}\times9\text{cm}=33\text{cm}$
$\therefore$ Height of the stack = 33cm.
View full question & answer→Question 443 Marks
Cloth is being sold at $\text{Rs. }45\frac{1}{2}$ per metre. What is the cost of $5\frac{3}{5}$ metres of this cloth?
AnswerCost of 1 metre pf cloth
$=\text{Rs. }42\frac{1}{2}=\text{Rs. }\frac{85}{2}$
Cost of $5\frac{3}{5}$ metres $\text{Rs. }\frac{85}{2}\times5\frac{3}{5}$
$=\text{Rs. }\Big(\frac{85}{2}\times\frac{28}{5}\Big)$
$=-\text{Rs. }(17\times14)=\text{Rs. }238$
View full question & answer→Question 453 Marks
One tin holds $=12\frac{3}{4}\text{ litres}$ of oil. How many litres of oil can 26 such tins hold?
AnswerOne tin holds oil $=12\frac{3}{4}\text{ litres}$
$=\frac{51}{4}\text{ litres}$
$\therefore$ 26 tins will hold oil $=\frac{51}{4}\times26\text{ litres}$
$=\frac{51\times13}{2}=\frac{663}{2}\text{ litres}$
$=331\frac{1}{2}\text{ litres}$
View full question & answer→Question 463 Marks
Find the sum:
$\frac{7}{12}+\frac{11}{16}+\frac{9}{24}$
Answer$\frac{7}{12}+\frac{11}{16}+\frac{9}{24}$LCM of 12, 16, 24 = 48
$\frac{7}{12}=\frac{7\times4}{12\times4}=\frac{28}{48}$
$\frac{11}{16}=\frac{11\times3}{16\times3}=\frac{33}{48}$
$\frac{9}{24}=\frac{9\times2}{24\times2}=\frac{18}{48}$
$\therefore=\frac{7}{12}+\frac{11}{16}+\frac{9}{24}$
$=\frac{28}{48}+\frac{33}{48}+\frac{18}{48}$
$=\frac{28+33+18}{48}=\frac{79}{48}=1\frac{31}{48}$
View full question & answer→Question 473 Marks
The cost of $5\frac{1}{4}\text{kg}$ of mangoes is Rs. 189. At what rate /kg are the mangoes being sold?
AnswerCost of $5\frac{1}{4}\text{kg}$ of mangoes = Rs. 189
Cost of 1kg of mango
$\text{Rs. }\Big(189\div5\frac{1}{4}\Big)$
$\text{Rs. }\Big(189\div\frac{21}{4}\Big)$
$\text{Rs. }\Big(189\times\frac{4}{21}\Big)$
$\Big[\because\text{ Reciprocal of }\frac{21}{4}=\frac{4}{21}\Big]$
$=\text{Rs. }(9\times4)=\text{Rs. }36$
Hence, the mangose are being sold at 36/kg.
View full question & answer→Question 483 Marks
Sapna earns Rs. 24000 per month. She spends $\frac{7}{8}$ of her income and deposits rest of the money in a bank. How much money does she deposit in the bank each month?
AnswerSapna total income for one month = Rs. 24000
Amount spent $=\frac{7}{8}$ of her income
$=\frac{7}{8}\times24000$
= Rs. (7 × 3000) = Rs. 21000
Amount deposited in the bank per month
= Rs. 24000 - 21000 = Rs. 3000
View full question & answer→Question 493 Marks
18 boxes of nails weigh equally and their total weight is $49\frac{1}{2}\text{kg.}$ How much does each box weight?
AnswerTotal weight of 18 boxes
$=49\frac{1}{2}\text{kg}=\frac{99}{2}\text{kg}$
$\therefore$ Weight of 1 box $=\Big(\frac{99}{2}\div18\Big)\text{kg}$
$=\frac{99}{2}\times\frac{1}{18}=\frac{11}{2\times2}=\frac{11}{4}\text{kg}$
$=2\frac{3}{4}\text{kg}$
View full question & answer→Question 503 Marks
A rectangular sheet of paper is $15\frac{3}{4}\text{cm}$ long and $12\frac{1}{2}\text{cm}$ wide. Find its perimeter.
AnswerLength of rectangular sheet $\text{(l)}=15\frac{3}{4}\text{cm}=\frac{63}{4}\text{cm}$
and width $\text{(b)}12\frac{1}{2}\text{cm}=\frac{25}{2}\text{cm}$
$\therefore$ Its perimeter $=2(\text{l+b})$
$=2\Bigg[\frac{63}{4}+\frac{25}{2}\Bigg]$
$=2\Bigg[\frac{63+50}{4}\Bigg]$
$=2\times\frac{113}{4}=\frac{113}{2}\text{cm}$
$=56\frac{1}{2}\text{cm}$
View full question & answer→Question 513 Marks
Amit weighs 35kg. His sister Kavita’s weight is$\frac{3}{5}$ of Amit's weight. How much does Kavita weigh?
AnswerWeight of Amit = 35kg.
Weight of kavita $=\frac{3}{5}$ of Amit's weight
$=\frac{3}{5}\times35\text{kg}=21\text{kg}$
View full question & answer→Question 523 Marks
Rohit takes $=4\frac{4}{5}\text{ minutes}$ to make a complete round of a circular park. How much time will he take to make 15 rounds?
AnswerTime taken in one round $=4\frac{4}{5}\text{ minutes}$
$=\frac{24}{5}\text{ minutes}$
$\therefore$ Time taken in 15 round $=\frac{24}{5}\times15\text{ minutes}$
= 72 minutes
= 1 hour 12 minutes.
View full question & answer→Question 533 Marks
Find the difference:
$\frac{5}{6}-\frac{3}{4}$
Answer$\frac{5}{6}-\frac{3}{4}$
LCM of 6 and 4 = 12
$\therefore\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}$
$\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$
$\therefore\frac{5}{6}-\frac{3}{4}=\frac{10}{12}-\frac{9}{12}$
$=\frac{10-9}{12}=\frac{1}{12}$
View full question & answer→Question 543 Marks
Arrange the following fractions in ascending order:
$\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$
Answer$\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$Writing them into like fractions, LCM of 5, 10, 15, 20 = 60
Now $\frac{4}{5}=\frac{4\times12}{5\times12}=\frac{48}{60}$
$\frac{7}{10}=\frac{7\times6}{10\times6}=\frac{42}{60}$
$\frac{11}{15}=\frac{11\times4}{15\times4}=\frac{44}{60}$
$\frac{11}{12}=\frac{11\times3}{12\times3}=\frac{33}{36}$
Now, arranging them in ascending order,
$\frac{42}{60}<\frac{44}{60}<\frac{48}{60}<\frac{51}{60}$
or $\frac{7}{10}<\frac{11}{15}<\frac{4}{5}<\frac{17}{20}$
View full question & answer→Question 553 Marks
Find the difference:
$7-4\frac{2}{3}=\frac{7}{1}-\frac{14}{3}$
Answer$7-4\frac{2}{3}=\frac{7}{1}-\frac{14}{3}$
LCM of 1 and 3 = 3
$\therefore\frac{7\times3}{1\times3}=\frac{21}{3}$
$\frac{7}{1}-\frac{14}{3}=\frac{21}{3}-\frac{14}{3}$
$=\frac{21-14}{3}=-\frac{7}{3}=2\frac{1}{3}$
View full question & answer→