Quantitative Aptitude

Ratio and Proportion

775 Questions
All Dividing a total in a given ratio 393 Income, expenditure, and equal-savings equations 117 Ratio changes with constant sum/difference 89 Combining ratios 72 Finding a missing term in a proportion 54 Direct, inverse, and power variation 29 Mean proportional 9 Compound, duplicate, and root ratios 8 Componendo and dividendo 2

Ratio and Proportion Questions

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditures are in the ratio 5 : 7. If each saves Rs. 5, 000 then, find their annual incomes.

  1. A = Rs. 22,000 and B = Rs. 30,000

  2. A = Rs. 30,000 and B = Rs. 40,000

  3. A = Rs. 50,000 and B = Rs. 70,000

  4. A = Rs. 40,000 and B = Rs. 20,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the annual incomes of A and B be $ 3x $ and $ 4x $

And the annual expenditures of A and B be $ 5y $ and $ 7y $

Since each of them saves $ Rs  5000 $. 

$ 3x-5y = 5000 $ ----- (1)
$4x-7y = 5000 $ ---- (2)

Multiplying equation  $ (1) $ with $ 4 $ we get, $ 12x - 20y = 20000 $ ----- equation $ (3) $

Multiplying equation  $ (2) $ with $ 3 $ we get, $ 12x-21y=15000 $ ----- equation $ (4) $

Subtracting equation $ (4) $ from $ (3) $, we get $ y = 5000 $

Substituting $ y = 5000 $ in the equation $ (1) $, we get $ 3x-5(5000) = 5000 = x = 10000 $

Hence,, annual income of A $ = 3x =$ Rs $30000 $ and of B $ = 4x =$ Rs $ 40000 $

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A sum of money is divided into $2$ parts such that $6$ times of one part added to $15$ times the other gives $8$ times the whole. What is the ratio of one part to the other?

  1. $5 : 2$
  2. $4 : 9$
  3. $7 : 6$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let two parts of money  be Rs. $ x$ and Rs. $ y$.
Then, according to the given condition,

$\Rightarrow 6x+15y=8(x+y)$
$\Rightarrow 6x+15y=8x+8y$
$\Rightarrow 2x=7y$
$\Rightarrow \displaystyle \frac{x}{y}=\frac{7}{2}$
$\Rightarrow  x:y=7:2$

Hence, option D.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Some one rupee, $50$ paise and $25$ paise coins make up $Rs.\,93.75$ and their numbers are in the ratio $3\,\colon\,4\,\colon\,5$. Find the number of each type of coins.

  1. $\;40,70,75$
  2. $\;46,58,75$
  3. $\;42,56,70$
  4. $\;45,60,75$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the numbers of one rupee, $50:p$ and $25:p$ coins be $3x,4x$ and $5x$ respectively. Then,
$\;\;\;\;\;\;\;\;3x\times1+4x\times0.50+5x\times0.25=93.75$
$\;\;\;\;\;\;\;\;\Rightarrow\,3x+2x+1.25x=93.75$
$\;\;\;\;\;\;\;\;\Rightarrow\,6.25x=93.75$
$\;\;\;\;\;\;\;\;\Rightarrow\,x=\displaystyle\frac{93.75}{6.25}=\displaystyle\frac{9375}{625}=15$.
$\;\;\;\;\;\;\;\;\therefore\;$The number of onerupee, $50\ p$ and $25\ p$ coins are $45,60$ and $75$ respectively.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Divide $Rs.\,715$ in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}$.

  1. $\;Rs.\,350,\,Rs.\,250,\,Rs.\,115$
  2. $\;Rs.\,300,\,Rs.\,250,\,Rs.\,165$
  3. $\;Rs.\,330,\,Rs.\,220,\,Rs.\,165$
  4. $\;Rs.\,400,\,Rs.\,260,\,Rs.\,55$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio in which Rs $715$ is to be divided is $6:4:3$.

So, we have $13x = 715$ or $x = 55$
So, $6x$ will be Rs. $330$
$3x$ will be Rs $165$ and $4x$ is Rs $220$.

So, the answer is option $C$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

An amount of money is to be distributed among $A,B\,$and$\,C$ in the ratio $3\,\colon\,1\,\colon\,5$. The difference between $B's$ share and $C's$ share is $Rs.\,3600$. What is the total of $A's$ share and $B's$ share?

  1. $\;Rs.\,5400$
  2. $\;Rs.\,3600$
  3. $\;Rs.\,2700$
  4. $\;Rs.\,1800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the shares of $A,B\,$and$\,C$ be $3x,x\,$and$\,5x$ respectively.
$\;\;\;\;\;\;\;$ Given, $5x-x=3600\;\;\;\;\;\Rightarrow\;4x=3600$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\Rightarrow\,x=900$
$\;\;\;\;\;\;\;\;\therefore\;A's\;share+B's\;share=Rs.\,3\times900+Rs.\,900$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=Rs.\,2700+Rs.\,900$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\,Rs.\,3600$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A certain sum of money is divided between $P$ and $Q$ in the ratio $3\displaystyle\frac{1}{2}\,\colon\,5\displaystyle\frac{1}{2}$. If $P$ gets $Rs.\,180$ less than $Q$, then what is the share of $Q$?

  1. $\;Rs.\,315$
  2. $\;Rs.\,495$
  3. $\;Rs.\,630$
  4. $\;Rs.\,810$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Q's share be Q, and P's share be $(Q - 180)$


P : Q is $7 : 11$

    $\dfrac { Q -  180 }{ Q } =\dfrac { 7 }{ 11 } $
$11Q - 1980=\quad 7Q$
               $ 4Q= 1980$
                 $Q = 495$

So, Q is Rs $495$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The ratio of the monthly income to the saving of a family is $9\,\colon\,2$. If the monthly income of the family is $Rs.\,2700$, then its monthly expenditure will be

  1. $\;Rs.\,1800$
  2. $\;Rs.\,2209.09$
  3. $\;Rs.\,2100$
  4. $\;Rs.\,1600$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the monthly savings of the family be $Rs.\,x$.
Then,$\displaystyle\frac{9}{2}=\displaystyle\frac{2700}{x}\;\Rightarrow\;\;\;x=600$
$\therefore$ Monthly expenditure$=Rs.\,2700-Rs.\,600$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=Rs.\,2100$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A company makes a profit of $Rs.\,9,00,000$. $20\%$ of which is paid as taxes. If the rest is divided among the partners $P,Q\,and\,R$ in the ratio $1\,\colon\,1\displaystyle\frac{1}{2}\colon2$, then the share of $P,Q$ and $R$ are respectively.

  1. $\;2,40,000;\,3,20,000;\,1,60,000$
  2. $\;3,20,000;\,2,40,000;\,1,60,000$
  3. $\;1,60,000;\,3,20,000;\,2,40,000$
  4. $\;1,60,000;\,2,40,000;\,3,20,000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Amount to be paid in taxes $=20\%$ of $Rs.\,9,00,000=Rs.\,1,80,000$
$\;\;\;\;\;\;\;$ Amount to be distributed among $P,Q\,and\,R=9,00,000-1,80,000=7,20,000$.
$\;\;\;\;\;\;\;\therefore\;Let\;the\;shares\;of\;P,Q\,and\,R\;be\,x,\displaystyle\frac{3x}{2}$ and $2x$ respectively. 

Then,
$\;\;\;\;\;\;\;\;x+\displaystyle\frac{3x}{2}+2x=7,20,000\;\Rightarrow\;\;x=Rs.\,1,60,000$.
$\;\;\;\;\;\;\;\;The\;share\;of\;P,Q\,and\,R\;are\;Rs.\,1,60,000,Rs.\,2,40,000\,and\,Rs.\,3,20,000$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A sum of money is divided among Peter, Anita and Janet in the ratio $13\colon12\colon7$. Calculate how much Anita gets, if the amount Peter gets more than Janet is $Rs.\,360$?

  1. $\;Rs.\,180$
  2. $\;Rs.\,640$
  3. $\;Rs.\,720$
  4. $\;Rs.\,480$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of the money divided among  Peter, Anita and Janet is $=13:12:7$
Difference of the ratio between Peter and Janet $=13-7=6$
If difference between Peter and Janet is $6$ then Anita gets $=6$
If the difference between Peter and Janet is $Rs.360$ then Anita gets $=\dfrac{12}{6}\times 360=720  Rs.$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Divide 170 into three parts such that the first part is 10 more than the second and its ratio with the third part is 2:5.

  1. $40, 30, 100$
  2. $20, 30, 100$
  3. $40, 50, 100$
  4. $50, 30, 100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the first part =x. Then,
Second part = x-10
$\displaystyle \frac {First \ part}{Third \ part} = \frac {2}{5} \Rightarrow Third \ part = \frac {5x}{2} $
Given, $ \displaystyle x= x - 10 + \frac {5x}{2}= 170 \Rightarrow 2x+ 2x - 20 + 5x = 340 \Rightarrow 9x = 360 \Rightarrow x = 40$
$\displaystyle \therefore $ The  three  parts  are  40, 40- 10 , 5 $ \displaystyle \times \frac {40}{2}$, i.e. , 40, 30, 100

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

$A$ and $B$ have a monthly incomes in the ratio $5\,\colon\,6$ and monthly expenditures in the ratio $3\,\colon\,4$. If they save $Rs.\,1800$ and $Rs.\,1600$ respectively, find the monthly income of $B$.

  1. $\;Rs.\,3400$
  2. $\;Rs.\,2700$
  3. $\;Rs.\,1720$
  4. $\;Rs.\,7200$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the monthly incomes of $A$ and $B$ be $Rs.\,5x$ and $Rs.\,6x$ respectively.
$\;\;\;\;\;\;\;\;$ Then, $\displaystyle\frac{5x-1800}{6x-1600}=\displaystyle\frac{3}{4}$
$\;\;\;\;\;\;\;\;\;\Rightarrow\,20x-7200=18x-4800$
$\;\;\;\;\;\;\;\;\;\Rightarrow\,2x=2400\;\;\Rightarrow\;\;x=1200$
$\therefore$ Monthly income of B$=6\times\,Rs.\,1200=Rs.\,7200$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A person divided Rs. $10,800$ among his three sons in the ratio $3\colon4\colon5$. Second son kept Rs. $1000$ for himself, gave Rs. $600$ to his wife and divided the remaining money among his two daughters in the ratio $11\colon9$. Then one of his daughter's received

  1. Rs. $1000$
  2. Rs. $1050$
  3. Rs. $1100$
  4. Rs. $1150$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Second son's share $=\displaystyle\frac{4}{(3+4+5)}\times $Rs. $10,800$
$=\dfrac{4}{12}\times $ Rs $,10,800=$ Rs. $3600$
Remaining money with him $=$ Rs. $3600-$ Rs. $(1000+600)$
$=$ Rs. $2000$.
Both the daughter's share are $\displaystyle\frac{11}{20}\times$ Rs. $2000 $ and $\displaystyle\frac{9}{20}\times $ Rs. $2000$

$=$ Rs. $1100$ and Rs. $900$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The incomes of $A$ and $B$ are in the ratio $5 : 3.$ The expenses of $A, B$ and $C$ are in the ratio $8 : 5 : 2.$ If C spends $Rs. 2000$ and $B$ saves $Rs. 700,$ then $A$ saves

  1. $Rs. 1500$
  2. $Rs. 1000$
  3. $Rs. 500$
  4. $Rs. 250$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the expenses of A, B and C be Rs. 8x, Rs. 5x and Rs. 2x respectively. Given, 2x = 2000
$\Rightarrow x = Rs. 1000$
$\Rightarrow$ B's expenses $= 5 \times Rs. 1000 = Rs. 5000$,
A's expenses $=Rs. 8000$
Given, B's saving $= Rs. 700$
$\Rightarrow $ B's income $= Rs. 5000 + Rs. 700 = Rs. 5700$
Given, A's income : B's income = 5 : 3
$\Rightarrow \displaystyle \frac{\text{A's income}}{5700} = \frac{5}{3}$
$\Rightarrow $ A's income $= \displaystyle \frac{5}{3} \times Rs. 5700 = Rs. 9500$
$\therefore$ A's savings $= Rs 9500 - Rs. 8000 = Rs. 1500$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A sum of money is delivered among $A, B, C$ and $D$ in the ratio $3:4:9:10$. If the share of $C$ is Rs. $2580$ more than the share of $B$, What is the total amount of money of $A$ and $D$ together ?

  1. 6400

  2. 6708

  3. 6700

  4. 6510
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given ratio : $3 : 4 : 9 : 10$
Let $A$ share $= 3x$
$B$ share $= 4x$
$C$ share $= 9x$
$D$ share $ = 10x$
Given, $C$ share is $2580$ more than $B$ share i.e.
$9x - 2580 = 4x$
$5x = 2580$
$x = 516$
So, $A$ share $= 3x = 516\times 3 = 1548$
$D$ share  $= 10x = 516\times 10 = 5160$
$A + D = 1548 + 5160 =$ Rs. $6708$