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 direct proportion and inverse proportion rule of three types of proportions direct proportion

A sum is divided among four persons in the ratio $3\,\colon\,4\,\colon\,5\,\colon\,8$. If the second largest share is  Rs$\,2500$, what is the total sum?

  1. Rs $10000$
  2. Rs $15000$
  3. Rs $1000$
  4. Rs $1500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The share is divided in the ratio $3:4:5:8$

$\therefore$ the second largest share is $5$.
Second largest share$\,=\displaystyle\frac{5}{(3+4+5+8)} \times$ Total share 
 $=\displaystyle\frac{5}{20}\times $ Total sum $=\displaystyle\frac{1}{4}\times $  Total sum

Given, second largest share $=Rs.2500$ 
 $\therefore \displaystyle\frac{1}{4}\times$ Total sum $Rs.2500$
 $\Rightarrow$ Total sum $=Rs.10,000$.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

One year ago, the ratio between Ram's and Shyam's salaries was $3 : 5$. The ratio of their individual salaries of last year and present year are $2 : 3$ and $4 : 5$ respectively. If their total salaries for the present year is $Rs. 8600$, find the present salary of Ram ?

  1. $3200$
  2. $3600$
  3. $4000$
  4. $4400$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let past salaries be 3x and 5x. Present salaries are (3/2)*3x = 4.5x and (5/4)*5x = 6.25x. Total = 10.75x = 8600. x = 800. Ram's present salary = 4.5 * 800 = 3600.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

If the price of a pen increases from Rs $15$ to Rs $20$, then the price has increased in the ratio of?

  1. $4 : 3$
  2. $1 : 2$
  3. $3 : 4$
  4. $9 ; 8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

New price $= 20$
Old price $= 15$
Multiplying ratio
$\dfrac {\text {new price}}{\text {old price}} = \dfrac {20}{15} = \dfrac {4}{5}$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The multiplying ratio which changes Rs $90$ into Rs $63$ is ____

  1. $5 : 9$
  2. $3 : 4$
  3. $6 : 8$
  4. $7 : 10$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Final quantity $= 63$
Original quantity $= 90$
Multiplying ratio
$\dfrac {\text {Final quantities}}{\text {Original quantity}} = \dfrac {63}{90} = \dfrac {7}{10}$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

In what ratio we must increase Rs. $750$ to obtain Rs. $1000$?

  1. $1 : 2$
  2. $5 : 6$
  3. $4 : 3$
  4. $7 : 8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original quantity $= 750$
Final quantity $= 1000$

Multiplying ratio:
$\dfrac {\text {final quantity}}{\text {original quantity}} = \dfrac {1000}{750} = \dfrac {4}{3}$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Increasing Rs $40$ in the ratio $5 : 4$ we get?

  1. $10$
  2. $60$
  3. $50$
  4. $80$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Increasing Rs $40$ in the ratio $5.4$ implies that the ratio of the new quantity to the old quantity is $5 : 4$.
$\therefore$ Let the increased quantity be x
$\therefore \dfrac {\text {New amount}}{\text {original amount}} = \dfrac {x}{40} = \dfrac {5}{4}$
$\therefore x = 50$
that is the increased quantity is $50$

Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If $40$%of a number is equal to two-third of another number, what is the ratio of first number to the second numbers?

  1. 2:5

  2. 3:7

  3. 5:3

  4. 7:3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$(l-m) (lm+l+x^{2})=0$
 Let the number be $x _{1} y$
Given :- $40\% $ of $(x) = \dfrac{2}{3}$ of $(y)$
to find :-$\dfrac{x}{y}= ?$
$\dfrac{40}{100} \times x = \dfrac{2}{3} \times y$
$\dfrac{x}{y}= \dfrac{2}{3} \times \dfrac{100}{40}$
$\Rightarrow \dfrac{x}{y}= \dfrac{5}{3}$
Multiple choice maths discount and commission commission and rebate commission deductions from earnings

Prices register an increase of $10\%$ on food grains and $15\%$ on other items of expenditure. If the ratio of an employees expenditure on food grains and other items be $2 : 5$, by how much should his salary be increased in order that he may maintain the same level of consumption as before his present salary being Rs. $2590$

  1. Rs. $ 323.75$
  2. Rs. $ 350$
  3. Rs. $ 360.50$
  4. Rs. $ 351.50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given that the expenses on food : other items $=2 : 5$.

His salary $=$ Rs. $2590$.
$\therefore $ expenses on food $=$ Rs. $\dfrac { 2 }{ 5+2 } \times 2590=$ Rs. $740$ and 
the expenses on other items $=$ Rs. $(2590-740)=$ Rs. $1850$.
Now the rise in price for rice at $10\%=$ Rs. $740\times \dfrac { 10 }{ 100 } =$ Rs. $74$ and
the rise in price for other items at $15\%=$ Rs. $1850\times \dfrac { 15 }{ 100 } =$ Rs. $277.5.$ 
$\therefore $ the net rise in expenses $=$ Rs. $(74+277.5)=$ Rs. $351.5$.
$\therefore $ his salary should be increased by Rs. $351.5$ to cope with the present situation.

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

Mark the correct alternative of the following.
If A, B, C divide Rs. $1200$ in the ratio $2 : 3 : 5$, then B's share is?

  1. Rs. $240$
  2. Rs. $600$
  3. Rs. $380$
  4. Rs. $360$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since they divide Rs. $1200$ in the ratio $2:3:5$ then let shares of them will be $2x,3x$ and $5x$.

Then according to the problem we get,
$2x+3x+5x=1200$
or, $x=120$.
So share of B is Rs. $120\times 3=360$.

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

 The third proportion between : $2$ and $8$

  1. $4$
  2. $3$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued proportion, and c is the third proportional of a and b.

Here, $ {b}^{2} = ac $ or $ b = \sqrt {ac} $

So, for $ 2, 8 $, the third proportional is $ b = \sqrt {ac} = \sqrt {2 \times 8} = \sqrt {16} = 4 $

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

By mistake instead of dividing Rs. $117$ among $A,B$ and $C$ into the ratio $\displaystyle \frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ , it was divided in the ratio of $2:3:4$ . Who gains the most and by how much?

  1. $A, Rs. 28$
  2. $B, Rs. 3$
  3. $C, Rs. 20$
  4. $C, Rs. 25$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To convert $\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ into normal ratio, multiply each fraction by the LCM$(2,3,4) = 12$

$\displaystyle= 12\times \frac{1}{2}:12\times\frac{1}{3}:12\times\frac{1}{4}$
= $\displaystyle 6:4:3 $
Thus, A would have got $\displaystyle \frac{6}{6+4+3} \times 117 = 54$

B would have got $\displaystyle \frac{4}{6+4+3} \times 117 = 36$

And C would have got $\displaystyle \frac{3}{6+4+3} \times 117 = 27$

Instead Rs. $117$ have been divided in the ratio of $2:3:4$

A gets $\displaystyle \frac {2}{2+3+4} \times 117 = 26$

B gets $\displaystyle \frac {3}{2+3+4} \times 117 = 39$

C gets $\displaystyle \frac {4}{2+3+4} \times 117 = 52$

Thus, by changing the ratio,
A gained $26 - 54$ = -$28$
B gained $39 - 36$ = $3$
And C gained $52 - 27 = 25$
Thus, C's gain of $25$ is the most.

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

If $78$ is divided into three parts which are proportional to $1, \dfrac {1}{3}, \dfrac {1}{6}$, the middle part is

  1. $9\dfrac {1}{3}$
  2. $13$
  3. $17\dfrac {1}{3}$
  4. $18\dfrac {1}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $x + \cfrac {1}{3} x + \cfrac {1}{6}x = 78$

$\Rightarrow 9x = 468$
$\Rightarrow \cfrac {1}{3}x = \cfrac {468 }{9} \times \cfrac 13=17\cfrac {1}{3}$.

Multiple choice elements of accounts ratio analysis liquidity ratios accounting ratio's accounting ratios

If the current ratio is $2 : 1$ and working capital is $Rs. 60,000$, what is the value of the current assets?

  1. $Rs. 60,000$
  2. $Rs. 1,00,000$
  3. $Rs. 1,20,000$
  4. $Rs. 1,80,000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Current Ratio = Current Assets (C.A)/ Current Liabilities (C.L)  = $2/1$

So, CA= $2$ CL

Now, Working Capital = Current Assets(C.A) minus Current Liabilities (C.L) = $Rs.60000$
So, C.A - C.L = $60000$
       $2$ C.L-CL = $60000$
        C.L = $Rs. 60000$

Now, C.A = $2$ x $60000$ = $Rs. 120000$

Multiple choice elements of accounts ratio analysis liquidity ratios accounting ratio's accounting ratios

Given current ratio = $2.5$
Quick ratio = $1.5$
Net working capital = Rs $30,000$
What is the amount of current liabilities?

  1. $Rs20,000$
  2. $Rs30,000$
  3. $Rs50,000$
  4. $Rs60,000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Net working capital = Current assets - Current liabilities
$Rs. 30000$ = Current assets - Current liabilities
Therefore, Current assets = Current liabilities + $Rs. 30000$
Current ratio = Current assets/ Current liabilities
$2.5$ = [Current liabilities + $Rs. 30000$] / Current liabilities
 $2.5$ Current liabilities  = Current liabilities + $Rs. 30000$
Current liabilities = $Rs. 30000/ 1.5$
Therefore, Current liabilities = $Rs. 20000$
Multiple choice elements of accounts ratio analysis liquidity ratios accounting ratio's accounting ratios

Given current ratio = $2.5$
Quick ratio = $1.5$
Net working capital = Rs $30,000$
What is the amount of quick assets?

  1. $Rs 20,000$
  2. $Rs 30,000$
  3. $Rs 50,000$
  4. $Rs 60,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Net working capital = Current assets - Current liabilities
$Rs. 30000$ = Current assets - Current liabilities
Therefore, Current assets = Current liabilities + $Rs. 30000$
Current ratio = Current assets/ Current liabilities
$2.5$ = [Current liabilities + $Rs. 30000$] / Current liabilities
 $2.5$ Current liabilities  = Current liabilities + $Rs. 30000$
Current liabilities = $Rs. 30000/ 1.5$
Therefore, Current liabilities = $Rs. 20000$
Now,
Current assets = Current liabilities + $Rs. 30000$
                          = $Rs.20000 + Rs. 30000$
                          =$Rs. 50000$
Now, Quick Ratio = Quick Assets/ Current liabilities
                     $1.5$   = Quick Assets/ $20000$
Therefore,
                  Quick Assets = $Rs. 30000$