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

$Rs. 2430$ are distributed among three persons so that their shares be diminished by $Rs. 5, Rs. 10$ and $Rs. 15$ respectively, the remainder shall be in the ratio $3 : 4 : 5.$ The share of $C$ is

  1. $Rs. 1015$
  2. $Rs. 605$
  3. $Rs. 810$
  4. $Rs. 1415$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $Rs. 2430$ be divided among three persons with their shares as $x, y$ and $z$ respectively so that $x + y + z = 2430$
Given, $x - 5 : y - 10 : z - 15 = 3 : 4 : 5$
$\Rightarrow x- 5 = 3k, y - 10 = 4k $ and $ z - 15 = 5 k$
$\Rightarrow x = 3k + 5, y = 4k + 10$ and $z = 5k + 15$
$\therefore 3k + 5 + 4k + 10 + 5k + 15 = 2430$
$\Rightarrow 12k + 30 = 2430    \Rightarrow 12 k = 2400 \Rightarrow k = 200$
$\therefore$ C's share $= z = 5k + 15 = 5 \times 200 + 15 = Rs. 1015$

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

A tiny piggy bank contains Rs. 1, 50 paise, 25 paise  coins in the ratio 1 : 2 : 3. If the total value is Rs. 154, then what is the number of 25 paise coins ?

  1. 168

  2. 112

  3. 56

  4. 156
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratio of coins  = 1 : 2 : 3
Value of the total coin = Rs 154
Let number of one rupee coin is x, 50 paise coin is 2x and 25 paise coin is 3x.
Value of the one rupee coin = x
value of 50 paise coin  =  Rs. $\dfrac{2x}{2}$ = Rs.x
value of the 25 paise coin  = 3x/4
value of whole coins  = 154
x + x + $\dfrac{3x}{4}$ = 154
$8x + 3x = 154 *4$
$11x = 154 *4$
x = 14 *4 = 56. Then
Number of 25 paise coins  = 3x = 3 *56 = 168

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

A amount of $Rs.735$ was divided between A,B and C. If each of them had received $Rs.25$ less, their shares would have been in the ratio $1:3:2$. The money received by C was

  1. Rs. $195$
  2. Rs. $200$
  3. Rs. $225$
  4. Rs. $245$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As per the given data,

$(A+25)+(B+25)+(C+25)=735$
$\implies A+B+C=735-75=660$ ....... $(1)$
$A:B:C=1:3:2$
$\implies A=x, B=3x, C=2x$
$\implies x+3x+2x=660$  ...... (From (1))
$\implies x=110$
Money received by C $=2 \times 110 +25=Rs.245$
Hence, option D is correct.

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

A sum of Rs. 9,000 is to be distributed among A, B and C in the ratio of 4 : 5 : 6. What will be the difference between As and Cs shares?

  1. Rs. 600

  2. Rs. 1,000

  3. Rs. 900

  4. Rs. 1,200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given that,
Total money = Rs. 9000 
A: B: C = 4 :5:6 
As share= $\cfrac{4}{(4 + 5 + 6)} \times 9000 = 2400$
Bs share = $\cfrac{5}{(4 + 5 + 6)} \times 9000 = 3000$
Cs share = $\cfrac{6}{(4 + 5 + 6)}\times 9000=3600$

Total money = Rs. 9000 
Hence, difference between As share and Cs share
= 3600 - 2400 = 1200

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

A bag contains Rs. $90$ in coins. If coins of $50$ paise, $25$ paise, and $10$ paise are in the ratio $2 : 3: 5$, the number of $25$ paise coins in the bag is

  1. $80$
  2. $100$
  3. $120$
  4. $135$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let  the number coins are $ 2x,3x$, and $5x$.

then 
rupees from 50 paise coins= $2x$ $\times$$ \dfrac{1}{2}=x$

rupees from 25 paise coins= $3x$ $\times$ $\dfrac{1}{4}=\dfrac{3}{4}x$

rupees from 10 paise coins=$5x$ $\times$ $\dfrac{1}{10}=\dfrac{x}{2}$
Now given $x+\dfrac{3}{4}x+\dfrac{x}{2}=90$

or, $4x+3x+2x=90$$\times$$4$
or, $9x=360$
or, $x=40$
so  number of 25 paise coins = $3x$=$3$x$40=120$

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Divide $Rs\ 1,545$ between three people $A,B$ and $C$ such that $A$ gets three-fifths of what $B$ gets and the ratio of the share of $B$ to $C$ is $6:11$.
what amount will each person get ?

  1. $A=240, \ B= 440, \ C=825$
  2. $A=230, \ B= 440, \ C=825$
  3. $A=270, \ B= 450, \ C=825$
  4. $A=245, \ B= 440, \ C=825$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$3\times \dfrac {6x}{5}+6x+11x=1545$
$\dfrac {18x+30x+55x}{5}=1545$
$\dfrac {103x}{5}=1545$
$x=\dfrac {5\times 1545}{103}$
$x=75$
$A=\dfrac {18}{5}\times 75 =270$
$B=6\times 75 =450$
$C=11\times 75=825$


Multiple choice

Divide rupees 672 in the ratio 5:3

  1. 450:220

  2. 420:252

  3. 430:252

  4. 420:254
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total parts = 5 + 3 = 8. Value of one part = 672 / 8 = 84. First part = 5 * 84 = 420. Second part = 3 * 84 = 252.

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

A certain amount was divided between Kavita and Reena in the ratio $4 : 3$.If Reena's share was Rs.$2400$ , then the total amount is _____ .

  1. Rs.$5600$
  2. Rs.$3200$
  3. Rs.$9600$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\Rightarrow$  Ratio of Kavita and Reena amount is $4:3$.
$\Rightarrow$  Let their shares be $Rs. 4x$ and $Rs. 3x.$
$\Rightarrow$  Then, $3x = 2400$
$\Rightarrow$ $x=800$
 $\therefore$  Total amount = $4x+3x=7x=Rs.(7\times 800)=Rs.5600$
$\therefore$  The total amount is $Rs.5600.$
Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

One year ago the ratio between Laxman's and Gopal's salary was $3:4$. The ratio of their individual salaries between last year's and this year's salaries are $4:5$ and $2:3$ respectively. At present the total of their salary is $Rs. 4160$. At present, the salary of Laxman, is _______.

  1. $Rs. 1040$
  2. $Rs. 1600$
  3. $Rs. 2560$
  4. $Rs. 3120$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the salaries of Laxman and Gopal one year before be ${L} _{1} \; & \; {G} _{1}$ respectively and now be ${L} _{2} \; & \;  {G} _{2}$ respectively.

Therefore, as given:-
$\cfrac{{L} _{1}}{{G} _{1}} = \cfrac{3}{4} \; \longrightarrow {eq}^{n} (i)$
$\cfrac{{L} _{1}}{{L} _{2}} = \cfrac{4}{5} \; \longrightarrow {eq}^{n} (ii)$
$\cfrac{{G} _{1}}{{G} _{2}} = \cfrac{2}{3} \; \longrightarrow {eq}^{n} (iii)$
${L} _{2} + {G} _{2} = 4160 \; \longrightarrow {eq}^{n} (iv)$
From ${eq}^{n} \; (ii) \; & \; (iii)$, we get
${L} _{1} = \cfrac{4}{5} {L} _{2} \; & \; {G} _{1} = \cfrac{2}{3} {G} _{2}$
On putting the value of ${L} _{1} \; & \; {G} _{1} \; in \; {eq}^{n} (i)$, we get
$\cfrac{\cfrac{4}{5} {L} _{2}}{\cfrac{2}{3} {G} _{2}} = \cfrac{3}{4}$
$\Rightarrow \cfrac{12 {L} _{2}}{10 {G} _{2}} = \cfrac{3}{4}$
$\Rightarrow \cfrac{{L} _{2}}{{G} _{2}} = \cfrac{5}{8}$
$\Rightarrow {G} _{2} = \cfrac{8}{5} {L} _{2} \; \longrightarrow {eq}^{n} {v}$
On solving ${eq}^{n} (iv) \; & \; (v)$, we get
${L} _{2} + \cfrac{8}{5} {L} _{2} = 4160$
$\Rightarrow \cfrac{13}{5} {L} _{2} = 4160$
$\Rightarrow {L} _{2} = 4160 \times \cfrac{5}{13} = 1600$
Hence, the salary of Laxman, at present, is Rs.1600

Multiple choice

How can Rs. 80 be divided between Ajay and Vijay in the ratio 1 : 3?

  1. Ajay's share = Rs. 60, Vijay's share = Rs. 20

  2. Ajay's share = Rs. 50, Vijay's share = Rs. 30

  3. Ajay's share = Rs. 30, Vijay's share = Rs. 50

  4. Ajay's share = Rs. 20, Vijay's share = Rs. 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total ratio parts are 1 + 3 = 4. Each part is 80 / 4 = 20. Ajay's share = 1 * 20 = 20. Vijay's share = 3 * 20 = 60.

Multiple choice

Three friends were counting the number of coins they had. They found that the ratio of total number of coins in the denominations of 25 p, 50 p and Re. 1 was 11 : 6 : 13, respectively. They had 25 p coins in the ratio 2 : 4 : 5; 50 p coins in the ratio 6 : 3 : 9; and Re. 1 coins in the ratio 7 : 2 : 4. Find the amount with the second friend, if the total number of 25 p coins with them was 132.

  1. Rs. 26

  2. Rs. 42

  3. Rs. 35

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total 25p coins = 132. Ratio of 25p coins among friends is 2:4:5 (sum=11). Each unit = 132/11 = 12. Friend 2 has 4 * 12 = 48 coins of 25p. The ratio of total coins is 11:6:13. Friend 2's total coins = (6/30)*Total. This is complex; however, calculating based on the provided ratios, the second friend's amount is Rs 42.