Question 13 Marks
Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed $10 \frac{1}{2} \mathrm{~kg} ?$
Answer
$\begin{aligned} & \text { Total no. of parcels }=15 \\ & \text { Weight of each parcel }=10 \frac{1}{2} \mathrm{~kg}=\frac{21}{2} \mathrm{~kg} \\ & \text { Total weight }=15 \text { of } \frac{21}{2} \mathrm{~kg} \\ & =\frac{21}{2} \times 15 \mathrm{~kg} \\ & =\frac{315}{15} \\ & =157 \frac{1}{15} \mathrm{~kg} \\ & =157.5 \mathrm{~kg}\end{aligned}$
View full question & answer→Question 23 Marks
In a business, Ram and Deepak invest $\frac{3}{5}$ and $\frac{2}{5}$ of the total investment. If Rs. 40,000 is the total investment, calculate the amount invested by each.
AnswerGiven: Total investment $=$ Rs. 40000
Ram's investment $=\frac{3}{5}$ of Rs. 40000
$ \begin{aligned} & =\frac{3}{5} \times 40000 \\ & =3 \times 8000 \\ & =\text { Rs. } 24000 \end{aligned} $
Deepak's investment $=\frac{2}{5}$ of Rs. 40000
$ \begin{aligned} & =\frac{2}{5} \times 40000 \\ & =2 \times 8000 \\ & =\text { Rs. } 16000 \end{aligned} $
View full question & answer→Question 33 Marks
When Krishna travelled $25 \mathrm{~km}$, he found that $\frac{3}{5}$ of his journey was still left. What was the length of the whole journey?
Answer$\frac{3}{5}$ of the total journey was left
$\therefore$ Journey travelled by him $=1-\frac{3}{5}$
$ =\frac{5-3}{5}=\frac{2}{5} $
$\therefore \frac{2}{5}$ of total journey $=25 \mathrm{~km}$
$\therefore$ Total journey $=25 \mathrm{~km} \times \frac{5}{2}=\frac{125}{2} \mathrm{~km}$
$=62 \frac{1}{2} \mathrm{~km}$
View full question & answer→Question 43 Marks
If $\frac{4}{5}$ of an estate is worth Rs. 42,000 , find the worth of the whole estate. Also, find the value of $\frac{3}{7}$ of
Answer
$\begin{aligned} & \frac{4}{5} \text { of an estate }=\text { Rs. } 42,000 \\ & \therefore \text { Total value of estate }=\text { Rs. } 42,000 \times \frac{5}{4} \\ & =\text { Rs. } 10,500 \times 5=\text { Rs. } 52,500 \\ & \text { and value of } \frac{3}{7} \text { of it }=\frac{3}{7} \text { of its value } \\ & =\frac{3}{7} \text { of } 52,500=\frac{3}{7} \times 52,500 \\ & =3 \times 7500=22,500\end{aligned}$
View full question & answer→Question 53 Marks
I spent $\frac{3}{5}$ of my savings and still have Rs. 2,000 left. What were my savings?
AnswerLett my saving $=1$, Part spent $=\frac{3}{5}$ of savings
$\therefore$ Part left $=1-\frac{3}{5}=\frac{5-3}{5}=\frac{2}{5}$ of savings
But he left $=$ Rs. 2000
$\therefore \frac{2}{5}$ of savings $=$ Rs. 2000
$\therefore$ Total savings $=$ Rs. $2000 \times \frac{5}{2}$
$=$ Rs. 5000
View full question & answer→Question 63 Marks
A man spends $\frac{2}{5}$ of his salary on food and $\frac{3}{10}$ on house rent, electricity, etc. What fraction of his salary is still left with him?
AnswerLet salary of $\operatorname{man}=$ Rs. 1
Amount spent on food $=\frac{2}{5}$ of Rs. $1=$ Rs. $\frac{2}{5}$
and amount spent house rent $=\frac{3}{10}$ of Rs. 1
$ =\text { Rs. } \frac{3}{10} $
Total amount spent $=$ Rs. $\frac{2}{5}+\frac{3}{10}=\frac{4+3}{10}=\frac{7}{10}$
$\therefore$ Amount left with him $=1-\frac{7}{10}=\frac{10-7}{10}=\frac{3}{10}$
View full question & answer→Question 73 Marks
The heights of two vertical poles, above the earth's surface, are $14 \frac{1}{4} \mathrm{~m}$ and $22 \frac{1}{3}$ respectively. How much higher is the second pole as compared with the height of the first pole?
AnswerHeight of one pole above earth's surface $=14 \frac{1}{4} \mathrm{~m}$
and height of $d=$ second pole $=22 \frac{1}{3}$
$\therefore$ Second pole is higher than the first pole
$ =22 \frac{1}{3}-14 \frac{1}{4}=\frac{67}{3}-\frac{57}{4} $
$ =\frac{268-171}{12}=\frac{97}{12} \mathrm{~m}=8 \frac{1}{12} \mathrm{~m} $
View full question & answer→Question 83 Marks
Simplify: $10 \frac{1}{8}$ of $\frac{4}{5} \div \frac{35}{36}$ of $\frac{20}{49}$
Answer$ 10 \frac{1}{8} \text { of } \frac{4}{5} \div \frac{35}{36} \text { of } \frac{20}{49} $
Using BODMAS
$ \frac{81}{8} \text { of } \frac{4}{5} \div \frac{35}{36} \text { of } \frac{20}{49} $
$ =\frac{81}{10}+\frac{25}{63} $
$ =\frac{81}{10} \times \frac{63}{25}=\frac{5103}{250} $
$ =20 \frac{103}{250} $
View full question & answer→Question 93 Marks
Simplify: $\left(\frac{1}{2}+\frac{2}{3}\right) \div\left(\frac{3}{4}-\frac{2}{9}\right)$
Answer
$\begin{aligned} & \left(\frac{1}{2}+\frac{2}{3}\right) \div\left(\frac{3}{4}-\frac{2}{9}\right) \\ & =\frac{3+4}{6} \div \frac{27-8}{36} \text {..(Using BODMAS) } \\ & =\frac{7}{6} \div \frac{19}{36} \\ & =\frac{7}{6} \times \frac{36}{19}=\frac{42}{19}=2 \frac{4}{19}\end{aligned}$
View full question & answer→Question 103 Marks
Simplify: $\frac{1}{4}\left(\frac{1}{4}+\frac{1}{3}\right)-\frac{2}{5}$
Answer
$\begin{aligned} & \frac{1}{4}\left(\frac{1}{4}+\frac{1}{3}\right)-\frac{2}{5} \\ & =\frac{1}{4}\left(\frac{3+4}{12}\right)-\frac{2}{5} \\ & =\frac{1}{4} \times \frac{7}{12}-\frac{2}{5} \\ & =\frac{7}{48}-\frac{2}{5} \\ & =\frac{35-96}{240}=\frac{-61}{240}\end{aligned}$
View full question & answer→Question 113 Marks
Simplify: $8-\left\{\frac{3}{2}+\left(\frac{3}{5}-\frac{1}{2}\right)\right\}$
Answer
$\begin{aligned} & 8-\left\{\frac{3}{2}+\left(\frac{3}{5}-\frac{1}{2}\right)\right\} \\ & =8-\left\{\frac{3}{2}+\frac{3}{5}-\frac{1}{2}\right\}=\frac{8}{1}-\frac{3}{2}-\frac{3}{5}+\frac{1}{2} \\ & =\frac{80-15-6+5}{10}=\frac{85-21}{10}=\frac{64}{10} \\ & =\frac{32}{5}=6 \frac{2}{5}\end{aligned}$
View full question & answer→Question 123 Marks
Simplify: $6+\left\{\frac{4}{3}+\left(\frac{3}{4}-\frac{1}{3}\right)\right\}$
Answer
$\begin{aligned} & 6+\left\{\frac{4}{3}+\left(\frac{3}{4}-\frac{1}{3}\right)\right\} \\ & =6+\left\{\frac{4}{3}+\frac{3}{4}-\frac{1}{3}\right\}=\frac{6}{1}+\frac{4}{3}+\frac{3}{4}-\frac{1}{3} \\ & =\frac{72+16+9-4}{12} \quad(\text { LCM of } 3,4=12) \\ & =\frac{97-4}{12}=\frac{93}{12}=\frac{31}{4}=7 \frac{3}{4}\end{aligned}$
View full question & answer→Question 133 Marks
What should be subtracted from $8 \frac{3}{4}$ to get $2 \frac{2}{3}$ ?
Answer
$\begin{aligned} & \text { The required number }=8 \frac{3}{4}-2 \frac{2}{3} \\ & \Rightarrow \frac{35}{4}-\frac{8}{3} \\ & \Rightarrow \frac{35 \times 3}{4 \times 3}-\frac{8 \times 4}{3 \times 4} \quad(\because \text { L.C.M. of } 4 \text { and } 3=12) \\ & \Rightarrow \frac{105-32}{12}=\frac{73}{12}=6 \frac{1}{12}\end{aligned}$
View full question & answer→Question 143 Marks
Simplify and reduce to a simple fraction:
$\frac{2}{3} \times 1 \frac{1}{4} \div \frac{3}{7} \text { of } 2 \frac{5}{8}$
Answer
$\begin{aligned} & \frac{2}{3} \times 1 \frac{1}{4} \div \frac{3}{7} \text { of } 2 \frac{5}{8} \\ & =\frac{2}{3} \times \frac{5}{4} \div \frac{3}{7} \text { of } \frac{21}{8} \\ & =\frac{2}{3} \times \frac{5}{4} \div \frac{9}{8} \quad \text { [Solving 'of'] } \\ & =\frac{2}{3} \times \frac{5}{4} \times \frac{8}{9} \text { [Solving ' } \div \text { '] } \\ & =\frac{20}{27}\end{aligned}$
View full question & answer→Question 153 Marks
Simplify: $3 \frac{3}{7} \div 1 \frac{1}{14}$
Answer
$\begin{aligned} & 3 \frac{3}{7} \div 1 \frac{1}{14} \\ & =\frac{24}{7} \times \frac{14}{15}=\frac{24 \times 14}{7 \times 15} \\ & =\frac{336}{105}=\frac{336 \div 21}{105 \div 21}(\mathrm{HCF} \text { of } 336 \text { and } 105=21) \\ & =\frac{16}{5}=3 \frac{1}{5}\end{aligned}$
View full question & answer→Question 163 Marks
Reduce to a single fraction:
$2 \frac{5}{8}-2 \frac{1}{6}+4 \frac{3}{4}$
Answer
$\begin{aligned} & 2 \frac{5}{8}-2 \frac{1}{6}+4 \frac{3}{4}=\frac{21}{8}-\frac{13}{6}+\frac{19}{4} \\ & =\frac{21 \times 3}{8 \times 3}-\frac{13 \times 4}{6 \times 4}+\frac{19 \times 6}{4 \times 6} \quad(\text { LCM of } 8,6,4=24) \\ & =\frac{63}{24}-\frac{52}{24}+\frac{114}{24} \\ & =\frac{63-52+114}{24} \\ & =\frac{177-52}{24}=\frac{125}{24}=5 \frac{5}{24}\end{aligned}$
View full question & answer→Question 173 Marks
Cost of $3 \frac{5}{7}$ litres of oil is ₹ $83 \frac{1}{2}$. Find the cost of one-litre oil.
AnswerCost of $3 \frac{5}{7}$ litres of oil $=$ ₹ $83 \frac{1}{2}$
$\therefore$ Cost of 1 liter oil $=$ ₹ $83 \frac{1}{2} \div 3 \frac{5}{7}$
= ₹ $\frac{167}{2} \div \frac{26}{7}$
= ₹ $\frac{167}{2} \times \frac{7}{26}$
= ₹ $\frac{1169}{52}$ = ₹ $22 \frac{25}{52}$
View full question & answer→Question 183 Marks
Reduce to a single fraction:
$2 \frac{1}{2}+2 \frac{1}{3}-1 \frac{1}{4}$
Answer
$\begin{aligned} & 2 \frac{1}{2}+2 \frac{1}{3}-1 \frac{1}{4} \\ & =\frac{5 \times 6}{2 \times 6}+\frac{7 \times 4}{3 \times 4}-\frac{5 \times 3}{4 \times 3} \quad(\text { LCM of } 2,3,4=12) \\ & =\frac{30}{12}+\frac{28}{12}-\frac{15}{12} \\ & =\frac{30+28-15}{12} \\ & =\frac{58-15}{12}=\frac{43}{12}=3 \frac{7}{12}\end{aligned}$
View full question & answer→Question 193 Marks
Reduce to a single fraction:
$\frac{2}{3}-\frac{1}{5}+\frac{1}{10}$
Answer$\frac{2}{3}-\frac{1}{5}+\frac{1}{10}$
$=\frac{2 \times 10}{3 \times 10}-\frac{1 \times 6}{5 \times 6}+\frac{1 \times 3}{10 \times 3} \quad($ LCM of $3,5,10=30)$
$=\frac{20}{30}-\frac{6}{30}+\frac{3}{30}=\frac{20-6+3}{30}$
$=\frac{23-6}{30}=\frac{17}{30}$
View full question & answer→Question 203 Marks
Reduce to a single fraction:
$\frac{1}{4}+\frac{5}{6}-\frac{1}{12}$
Answer
$\begin{aligned} & \frac{1}{4}+\frac{5}{6}-\frac{1}{12} \\ & =\frac{1 \times 3}{4 \times 3}+\frac{5 \times 2}{6 \times 2}-\frac{1}{12}(\text { LCM of } 4,6,12=12) \\ & =\frac{3}{12}+\frac{10}{12}-\frac{1}{12}=\frac{3+10-1}{12} \\ & =\frac{13-1}{12}=\frac{12}{2}=1\end{aligned}$
View full question & answer→Question 213 Marks
A rectangular park has length $=23 \frac{2}{3} \mathrm{~m}$ and breadth $=16 \frac{2}{3} \mathrm{~m}$. Find the area?
Answer
$\begin{aligned} & \text { Length of rectangular park }=23 \frac{2}{5} \mathrm{~m}=\frac{117}{5} \mathrm{~m} \\ & \text { Breadth of rectangular park }=16 \frac{2}{3} \mathrm{~m}=\frac{50}{3} \mathrm{~m} \\ & \therefore \text { Area of the park }=\mathrm{I} \times \mathrm{b} \\ & =\frac{117}{5} \times \frac{50}{3} \\ & =39 \times 10=390 \mathrm{~m}^2\end{aligned}$
View full question & answer→Question 223 Marks
A motorcycle runs $31 \frac{1}{4} \mathrm{~km}$ consuming 1 liter of petrol. How much distance will it run consuming $1 \frac{3}{5}$ liter of petrol?
AnswerDistance covered in 1 liter petrol
$ =31 \frac{1}{4} \mathrm{~km}=\frac{125}{4} \mathrm{~km} $
$\therefore$ Distance covered in $1 \frac{3}{5}$ liter of petrol
$ \begin{aligned} & =\frac{125}{4} \times \frac{8}{5} \\ & =\frac{1000}{20}=50 \mathrm{~km} \end{aligned} $
View full question & answer→Question 233 Marks
Reduce to a single fraction:
$\frac{3}{5}-\frac{1}{10}$
Answer
$\begin{aligned} & \frac{3}{5}-\frac{1}{10} \\ & =\frac{3 \times 2}{5 \times 2}-\frac{1}{10} \\ & =\frac{6}{10}-\frac{1}{10} \quad(\text { LCM of } 5 \text { and } 10=10) \\ & =\frac{6-1}{10}=\frac{5}{10}=\frac{1}{2}\end{aligned}$
View full question & answer→Question 243 Marks
Sugar costs $\text₹ 37 \frac{1}{2}$ per $\mathrm{kg}$. Find the cost of $8 \frac{3}{4} \mathrm{~kg}$ sugar.
AnswerCost of $1 \mathrm{~kg}$ sugar $=\text₹ 37 \frac{1}{2}$
$\therefore$ Cost of $8 \frac{3}{4} \mathrm{~kg}$ sugar
$=37 \frac{1}{2} \times 8 \frac{3}{4}$
$=\frac{75}{2} \times \frac{35}{4}$
$=\text₹ \frac{2625}{8}=\text₹ 328 \frac{1}{8}$
View full question & answer→Question 253 Marks
Insert two fractions between $\frac{5}{6}$ and $1 \frac{1}{5}$
Answerfraction between $\frac{5}{6}$ and $1 \frac{1}{5}$ or $\frac{5}{6}$ and $\frac{6}{5}$
$ =\frac{5+6}{6+5}=\frac{11}{11}=1 $
fraction between 1 and $\frac{6}{5}=\frac{1+6}{1+5}=\frac{7}{6}=1 \frac{1}{6}$
Hence, two fractions between $\frac{5}{6}$ and $1 \frac{1}{5}$ will be
1 and $1 \frac{1}{6}$
View full question & answer→Question 263 Marks
Insert two fractions between $\frac{5}{9}$ and $\frac{1}{4}$
Answerfraction between $\frac{5}{9}$ and $\frac{1}{4}$
$ =\frac{5+1}{9+4}=\frac{6}{13} $
fraction between $\frac{6}{13}$ and $\frac{1}{4}=\frac{6+1}{13+4}=\frac{7}{17}$
Hence, two fractions between $\frac{5}{9}$ and $\frac{1}{4}$
will be $\frac{6}{13}$ and $\frac{7}{17}$
View full question & answer→Question 273 Marks
Insert two fractions between 1 and $\frac{3}{11}$
Answerfraction between 1 and $\frac{3}{11}$
$ =\frac{1+3}{1+11}=\frac{4}{12}=\frac{1}{3} $
fraction between $\frac{1}{3}$ and $\frac{3}{11}=\frac{1+3}{3+11}=\frac{4}{14}=\frac{2}{7}$
Hence, two fractions between 1 and $\frac{3}{11}$
will be $\frac{1}{3}$ and $\frac{2}{7}$
View full question & answer→Question 283 Marks
Find the greater fraction:
$\frac{-2}{7} \text { and } \frac{-3}{10}$
Answer$\ln \frac{-2}{7}$ and $\frac{-3}{10}$, LCM of 7 and $10=70$
$\therefore \frac{-2}{7}=\frac{-2 \times 10}{7 \times 10}=\frac{-20}{70}$
and $\frac{-3}{10}=\frac{-3 \times 7}{10 \times 7}=\frac{-21}{70}$
It is clear from above that $\frac{-20}{70}>\frac{-21}{70}$
Hence $\frac{-20}{70}$ or $\frac{-2}{7}$ is greater..
View full question & answer→Question 293 Marks
Find the greater fraction:
$\frac{3}{8} \text { and } \frac{4}{9}$
Answer$\ln \frac{3}{8}$ and $\frac{4}{9}$, LCM of 8 and $9=72$
$\therefore \frac{3}{8}=\frac{3 \times 9}{8 \times 9}=\frac{27}{72}$
and $\frac{4}{9}=\frac{4 \times 8}{9 \times 8}=\frac{32}{72}$
It is clear from above that $\frac{32}{72}>\frac{27}{72}$
Hence $\frac{32}{72}$ or $\frac{4}{9}$ is greater.
View full question & answer→Question 303 Marks
Find the greater fraction:
$\frac{6}{7} \text { and } \frac{5}{9}$
Answer$\ln \frac{6}{7}$ and $\frac{5}{9}$, LCM of 7 and $9=63$
$\therefore \frac{6}{7}=\frac{6 \times 9}{7 \times 9}=\frac{54}{63}$
and $\frac{5}{9}=\frac{5 \times 7}{9 \times 7}=\frac{35}{63}$
It is clear from above that $\frac{54}{63}>\frac{35}{63}$
Hence $\frac{54}{63}$ or $\frac{6}{7}$ is greater.
View full question & answer→Question 313 Marks
Find the greater fraction:
$\frac{4}{5} \text { and } \frac{3}{10}$
Answer$\ln \frac{4}{5}$ and $\frac{3}{10}, \mathrm{LCM}$ of 5 and $10=10$
$\therefore \frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}$
and $\frac{3}{10}=\frac{3}{10}$
It is clear from above that $\frac{8}{10}>\frac{3}{10}$
Hence $\frac{4}{5}$ is greater.
View full question & answer→Question 323 Marks
Find the greater fraction:
$\frac{3}{5} \text { and } \frac{11}{15}$
Answer$\ln \frac{3}{5}$ and $\frac{11}{15}, \mathrm{LCM}$ of 5 and $15=15$
$ \therefore \frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15} $
$ \frac{11}{15}=\frac{11}{15} $
It is clear from above that $\frac{11}{15}>\frac{9}{15}$
Hence $\frac{11}{15}$ is greater.
View full question & answer→Question 333 Marks
Convert given fraction into a fraction with equal numerators:
$\frac{6}{13}, \frac{15}{23} \text { and } \frac{12}{17}$
Answer$\ln \frac{6}{13}, \frac{15}{23}$ and $\frac{12}{17}$, L.C.M. of 6,15 and $12=60$
$ \therefore \frac{6}{13}=\frac{6 \times 10}{13 \times 10}=\frac{60}{130} $
$ \frac{15}{23}=\frac{15 \times 4}{23 \times 4}=\frac{60}{92} $
and $\frac{12}{27}=\frac{12 \times 5}{17 \times 5}=\frac{60}{85}$
Hence the required fractions are $\frac{60}{130}, \frac{60}{92}$ and $\frac{60}{85}$
View full question & answer→Question 343 Marks
Convert given fraction into a fraction with equal numerators:
$\frac{8}{9} \text { and } \frac{12}{17}$
Answer$\ln \frac{8}{9}$ and $\frac{12}{17}$, L.C.M. of 8 and $12=24$
$ \therefore \frac{8}{9}=\frac{8 \times 3}{9 \times 3}=\frac{24}{27} $
$ \frac{12}{17}=\frac{12 \times 2}{17 \times 2}=\frac{24}{34} $
Hence the required fractions are $\frac{24}{27}$ and $\frac{24}{34}$
View full question & answer→Question 353 Marks
Convert given fraction into a fraction with equal denominator:
$\frac{2}{3}, \frac{5}{6} \text { and } \frac{7}{12}$
Answer$\ln \frac{2}{3}, \frac{5}{6}$ and $\frac{7}{12}:$ L.C.M of 3,6 and $12=12$
$ \begin{aligned} & \therefore \frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12} \\ & \frac{5}{6}=\frac{5 \times 2}{6 \times 2}=\frac{10}{12} \\ & \frac{7}{12}=\frac{7}{12} \end{aligned} $
Hence, the required fractions are $\frac{8}{12}, \frac{10}{12}$ and $\frac{7}{12}$
View full question & answer→Question 363 Marks
Convert given fraction into a fraction with equal denominator:
$\frac{5}{6} \text { and } \frac{7}{9}$
AnswerIn $\frac{5}{6}$ and $\frac{7}{9}:$ L.C.M of 6 and $9=18$
$ \begin{aligned} & \therefore \frac{5}{6}=\frac{5 \times 3}{6 \times 3}=\frac{15}{18} \\ & \frac{7}{9}=\frac{7 \times 2}{9 \times 2}=\frac{14}{18} \end{aligned} $
Hence, $\frac{15}{18}$ and $\frac{14}{18}$ are the required fractions.
View full question & answer→