Question 13 Marks
Two numbers are in the ratio $2 : 7. 11$ the sum of the numbers is $810$. Find the numbers.
AnswerTwo numbers are in the ratio $= 2 : 7$ Sum of the numbers $= 810$
We have,
Sum of the terms in the ratio $= 2 + 7 = 9$
First number $=\frac29\times810$
$=2\times90$
$=180$
Second number $=\frac{7}{9}\times810$
$=7\times90$
$=630$
View full question & answer→Question 23 Marks
Which ratio is larger in the following pairs? $4 : 7$ or $5 : 8$
Answer$4 : 7$ or $5 : 8$ $L.C.M.$ of $7$ and $8$ is $56$
$4:7=\frac{5\times8}{7\times8}$
$=\frac{32}{56}$
$5:8=\frac{5\times7}{8\times7}$
$=\frac{35}{56}$
$\frac{35}{56}>\frac{32}{56}$
$\frac58>\frac47$
$5:8>4:7$
View full question & answer→Question 33 Marks
The ratio of income to the expenditure of a family is $7 : 6$. Find the savings if the income is $Rs. 1400$.
AnswerThe ratio of income and expenditure $= 7 : 6$
$7x = 1400 x = 200$ Expenditure $= 6x = 6 \times 200 = Rs.1200$
Savings = Income - Expenditure $= 1400 - 1200 = Rs. 200$
View full question & answer→Question 43 Marks
The ages of two persons are in the ratio $5 : 7$. Eighteen years ago their ages were in the ratio $8 : 13$. Find their present ages.
AnswerLet the required ages be $5x$ and $7x.18$ years ago their age ratios,
$\frac{5\text{x}-18}{7\text{x}-18}=\frac{8}{13}$
$65\text{x}-13\times18=8\times\text{7x}-8\times18$
$65\text{x}-234=56\text{x}-144$
$65\text{x}-56\text{x}=234-144$
$9\text{x}=90$
$\text{x}=10$
Thus the ages are $5x = 5 × 10 = 50$ years
$7x = 7 × 10 = 70$ years.
View full question & answer→Question 53 Marks
Three numbers are in the ratio $2 : 3 : 5$ and the sum of these numbers is $800$. Find the numbers.
AnswerGiven that, Three numbers are in ratio $2 : 3 : 5$
Sum of these number $= 800$
Sum of the term of the ratio $= 2 + 3 + 5 = 10$
First number $=\frac{2}{10}\times800$ $= 160$
Second number $=\frac{3}{10}\times800$ $= 240$
third number $=\frac{5}{10}\times800$ $= 400$
View full question & answer→Question 63 Marks
Divide $Rs. 1350$ between Ravish and Shikha in the ratio $2 : 3$.
AnswerWe have, Sume of the terms of the ratio $= 2 + 3 = 5$
Ravish money $=\frac{2}{5}\times1350$ $=2\times270$ $=\text{Rs. }540$
Shikha money $=\frac35\times1350$ $=3\times270$ $=\text{Rs. }810$
View full question & answer→Question 73 Marks
If two numbers are in the ratio $6 : 13$ and their $L.C.M$ is $312$, find the numbers.
AnswerLet the required number be $6x$ and $13x$.
Then their $L.C.M.$ is $78x$. $78\text{x}=312$
$\text{x}=\frac{312}{78}$
$\text{x}=4$
Thus, The numbers are $6\text{x}=6\times4=24$
$13\text{x}=13\times4=54$
View full question & answer→Question 83 Marks
Which ratio is larger in the following pairs? $15 : 16$ or $24 : 25$
Answer$15 : 16$ or $24 : 25$ Now $L.C.M.$ of $16$ and $25$ is $400$
We have,
$15:16=\frac{15\times25}{16\times25}$
$=\frac{375}{400}$
$24:25=\frac{24\times16}{25\times16}$
$=\frac{384}{400}$
$\frac{384}{400}>\frac{375}{400}$
$\frac{15}{16}<\frac{24}{25}$
View full question & answer→Question 93 Marks
The ratio of monthly income to the savings of a family is $7 : 2$. If the savings be of $Rs. 500$, find the income and expenditure.
AnswerIt is given that,The ratio of income and savings is $7 : 2$
Savings
$2x = 500$
So, $x = 250$
Therefore,
Income $= 7 \times 250 = 1750$
Expenditure = Income - savings
$= 1750 - 500$
$= Rs. 1250$
View full question & answer→Question 103 Marks
The sides of a triangle are in the ratio $1 : 2 : 3$. If the perimeter is $36\ cm$, find its sides.
AnswerThe sides of the triangle are in the ratio $1 : 2 : 3$
Sum of the terms in the ratio $= 1 + 2 + 3 = 6$
Permeter $= 36\ cm$
First side $=\frac16\times36$
$=6\text{cm}$
Second side $=\frac26\times36$
$=12\text{cm}$
Third side $=\frac36\times36$
$=18\text{cm}$
View full question & answer→Question 113 Marks
In a class, one out of every six students fails. If there are $42$ students in the class, how many pass?
AnswerGiven,One out of $6$ student fails
$x$ out of $42$ students
$16=\frac{\text{x}}{42}$
$\text{x}=\frac{42}{6}$
$\text{x}=7$
Number of students who fail $= 7$ students
No of students who pass = Total students - Number of students who fail
$= 42 - 7 $
$= 35$ students.
View full question & answer→Question 123 Marks
The scale of a map is $1 : 4000000$. What is the actual distance between the two towns if they are 5cm apart on the map?
AnswerThe scale of map $= 1 : 4000000$
Let us assume the actual distance between towns is $x\ cm$
$1 : 4000000 = 5 : x$
$x = 5 \times 4000000 = 20000000\ cm$
$1\ km = 1000m$
$1m = 100cm$
Therefore
$x = 200\ km$
View full question & answer→Question 133 Marks
The ratio of income of a person to his savings is $10 : 1$. If his savings for one year is $Rs. 6000$, what is his income per month?
AnswerThe ratio of income of a person to his savings is $10 : 1$
Savings per month $=\frac{6000}{12}$ $= Rs. 500$
Then let income per month be $x x : 500 = 10 : 1 x = 500 \times 10 x = 5000$
View full question & answer→Question 143 Marks
If $x : y = 3 : 5$, find the ratio $3x + 4y : 8x + 5y.$
Answer$\text{x}:\text{y}=3:5$
$\frac{\text{x}}{\text{y}}=\frac35$
$5\text{x}=3\text{y}$
$\text{x}=\frac{3\text{y}}{5}$
$\text{3x}+\text{4y}:8\text{x}+5\text{y}$
$=\frac{3\times3\text{y}}{5}+4\text{y}:\frac{8\times3\text{y}}{5}+\text{5y}$
$=\frac{9\text{y}+20\text{y}}{5}:\frac{\text{24y}+\text{25y}}{5}$
$=\frac{29\text{y}}{5}:\frac{49\text{y}}{5}$
$=29\text{y}:49\text{y}$
$=29:49$
View full question & answer→Question 153 Marks
If $x : y = 8 : 9$, find the ratio $(7x - 4y) : 3x + 2y.$
Answer$\text{x}:\text{y}=8:9$
$\frac{\text{x}}{\text{y}}=\frac89$
$9\text{x}=\text{8y}$
$\text{x}=\frac{8\text{y}}{9}$
$7\text{x}-4\text{y}:3\text{x}+\text{2y}$
$=\frac{7\times\text{8y}}{9}-4\text{y}:\frac{3\times8\text{y}}{9}+2\text{y}$
$=\frac{56\text{y}-36\text{y}}{9}:\frac{\text{42y}}{9}$
$=20:42$
$=10:21$
View full question & answer→Question 163 Marks
The boys and the girls in a school are in the ratio $7 : 4$. If total strength of the school be $550$, find the number of boys and girls.
AnswerWe have,The boys girls is the ratio $7 : 4$
Sum of the terms in the ratio $= 7 + 4 = 11$
Total strength $= 550$
Boys strength $=\frac{7}{11}\times550$
$=7\times50$
$=350$ boys
Girls strength $=\frac{4}{11}\times550$
$=4\times50$
$=200$ girls
View full question & answer→Question 173 Marks
Which ratio is larger in the following pairs? $9 : 20$ of $8 : 13$
Answer$9 : 20$ or $8 : 13$ $L.C.M.$ of $20$ and $13$ is $260$
$9:20=\frac{9\times13}{20\times13}$
$=\frac{160}{260}$
$8:13=\frac{8\times20}{13\times20}$
$=\frac{117}{260}$
$\frac{160}{260}>\frac{117}{260}$
$\frac{8}{13}>\frac{9}{20}$
View full question & answer→Question 183 Marks
Give the equivalent ratios of $6 : 8$.
AnswerEquivalent ratios of $6 : 8$
$\frac{6\times2}{8\times2}=\frac{12}{16}$ (By multiplying numerator and denominator by $2$)
$= 6 : 8$
$\frac{\frac62}{\frac82}=\frac{3}{4}=3:4$ (By dividing numerator and denominator by $2$)
Two equivalent ratios
$3 : 4 = 12 : 16$
View full question & answer→Question 193 Marks
Two numbers are in the ratio $7 : 11$. If $7$ is added to each of the numbers, the ratio becomes $2 : 3$. Find the numbers.
AnswerLet the required numbers be $7x$ and $11x$.
If $7$ is added to each of the numbers it becomes
$\frac{7\text{x}+7}{11\text{x}+7}=\frac23$
$21\text{x}+21=22\text{x}+14$
$\text{x}=21-14=7$
Thus,
The numbers are $7x = 7 \times 7 = 49$
1$1x = 11 \times 7 = 77$
View full question & answer→Question 203 Marks
Which ratio is larger in the following pairs? $3 : 4$ or $9 : 16$
Answer$3 : 4$ or $9 : 16$
Now $L.C.M.$ of $4$ and $16$ is $16$
We have, $\frac34$ $=\frac{3\times4}{4\times4}$
$=\frac{12}{16}$ and $\frac{9}{16}=\frac{9}{16}$
Clearly, $12>9$
$\therefore\frac{3}{4}>\frac{9}{16}$
View full question & answer→Question 213 Marks
What should be added to each term of the ratio $7 : 13$ so that the ratio becomes $2 : 3$.
AnswerLet the number to be added be $x$ Then,
$\frac{7+\text{x}}{13+\text{x}}=\frac{2}{3}$
$(7+\text{x})3=2(13+\text{x})$
$3\text{x}-2\text{x}=26-21$
$\text{x}=5$
Hence the required number is $5$.
View full question & answer→Question 223 Marks
Divide $Rs. 2000$ among $P, Q, R$ in the ratio $2 : 3 : 5.$
AnswerWe have,Sum of the terms of the ratio $= 2 + 3 + 5 = 10$
$P$-share $=\frac{2}{10}$ $\times $ total mony
$=\frac{2}{10}\times2000$
$=2\times200$
$=\text{Rs. }400$
$Q$-share $=\frac{3}{10}$ $\times $ total money
$=\frac{3}{10}\times2000$
$=3\times200$
$=\text{Rs. }600$
$R$-share $=\frac{5}{10}$ $\times $ total money
$=\frac{5}{10}\times2000$
$=5\times200$
$=\text{Rs. }1000$
View full question & answer→Question 233 Marks
Two numbers are in the ratio $3 : 5$. If $8$ is added to each number, the ratio becomes $2 : 3$. Find the numbers.
AnswerLet the required numbers be $3x$ and $5x$ If $8$ is added to each other $\text{3x}+8:5\text{x}+8=2:3$
$\frac{3\text{x}+8}{\text{5x}+8}=\frac{2}{3}$
$3(3\text{x}+8)=2(5\text{x}+8)$
$\text{9x}+24=10\text{x}+16$
$10\text{x}-9\text{x}=24-16$
$\text{x}=8$
Thus the numbers are $3x = 3(8) = 24 5x = 5(8) = 40$
View full question & answer→Question 243 Marks
Which ratio is larger in the following pairs? $1 : 2$ or $13 : 27$
Answer$1 : 2$ or $13 : 27$ $L.C.M.$ of $2$ and $27$ is $54$
$1:2=\frac{1\times27}{2\times27}$
$=\frac{27}{54}$
$13:27=\frac{13\times2}{27\times2}$
$=\frac{26}{54}$
$\frac{27}{54}>\frac{26}{54}$
$\frac12>\frac{13}{27}$
View full question & answer→Question 253 Marks
Find the ratio of the price of pencil to that of ball pen, if pencil cost $Rs. 16$ per score and ball pen cost $Rs. 8.40$ per dozen.
AnswerOne score $= 20$ It is $Rs. 16$ per score for pencil
Pencil cost $=\frac{16}{20}$
$=\text{Rs. }0.80$
Cost of one dozen ball pen $= Rs. 8.40$
Cost of one ball pen $\frac{8.40}{12}$
$=\text{Rs. }0.70$
Ratio of peice of pencil to that of ball pen $=\frac{0.80}{0.70}$
$=\frac87$
View full question & answer→Question 263 Marks
The ratio of zinc and copper in an alloy is $7 : 9$. It the weight of the copper in the alloy is $11.7kg$, find the weight of the zinc in the alloy.
AnswerWe have,The ratio of zinc and copper in an alloy $= 7 : 9$
Weight of copper in the alloy $= 11.7kg$
$\text{9}\text{x}=11.7\text{kg}$
$\text{x}=\frac{11.7}{9}$
Weight of zinc in the alloy
$= 1.3 \times 7$
$= 9.10\ kg$
Therefore weight of zinc $= 9.10\ kg$
View full question & answer→