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Aptitude: Ratios & Proportion Solved Problems

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"Ratio and Proportion" is very important topic of Aptitude questions. This page deals with simple solved problems on Ratio and Proportion. To get a good score in BANK PO, Bank clerk, SBI Po etc examinations practicing these questions will be very useful.

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1.

A sum of money is to be distributed among A, B, C, D in the proportion of $5 : 2 : 4 : 3$. If C gets Rs. 1000 more than D, what is B's share?

A.

Rs. 500

B.

Rs. 1500

C.

Rs. 2000

D.

None of these

View Ans

 

Answer – (C)

Solution:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, $4x - 3x = 1000$
⇒ $x = 1000.$
B's share $= Rs. 2x = Rs. (2 × 1000) =$ Rs. 2000.

2.

A and B together have Rs. 1210. If $4/15$ of A's amount is equal to $2/5$ of B's amount, how much amount does B have?

A.

Rs. 460

B.

Rs. 484

C.

Rs. 550

D.

Rs. 664

View Ans

 

Answer – (B)

Solution:

${4/15}×A = {2/5}×B$
⇒ $A = ({2/5}×{15/4})B$
⇒ $A = {3/2}B$
⇒ $A/B = 3/2 $
⇒ $A : B = 3 : 2.$
B's share = Rs. $(1210×{2/5})=$ Rs. 484.

3.

A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs.2.40 the number of girls is

A.

35

B.

40

C.

45

D.

50

View Ans

 

Answer – (B)

Solution:

Step (i) Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
$x + y =  100$           -------------- (i)

Step (ii) A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
$3.60x +2.40y = 312$ -------------- (ii)

Step (iii)
Solving (i) and (ii)
$3.60 x + 3.60y = 360$       ------- Multiply (i) by 3.60
⇒ $3.60 x + 2.40y = 312$ --------- (ii)
$1.20y = 48$
$y = 48/1.20 = 40$

⇒ Number of girls = 40

4.

In a mixture 60 litres, the ratio of milk and water $2 : 1$. If the this ratio is to be $1 : 2$, then the quantity of water to be further added is:

A.

20 litres

B.

30 litres

C.

40 litres

D.

60 litres

View Ans

 

Answer - (D)

Solution:

Quantity of milk $= (60 × {2/3})$ litres $= 40$ litres.
Quantity of water in it $= (60- 40)$ litres $= 20$ litres.
New ratio $= 1 : 2$

Let quantity of water to be added further be x litres.
Then, $\text"milk : water" = (40/{20 + x})$

Now, $(40/{20 + x }) = 1/2 $
⇒ $20 + x = 80$
⇒ $x =$ 60

5.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A.

$2 : 5 $

B.

$3 : 5$

C.

$4 : 5 $

D.

$5 : 4$

View Ans

 

Answer – (C)

Solution:

Let the third number be x.

Then, first number $= 120%$ of $x = {120x}/100 = {6x}/ 5$
Second number $= 150%$ of $x = {150x}/100 = {3x}/ 2$
Ratio of first two numbers $= ({6x}/5 : {3x}/2) = 12x : 15x =$ 4 : 5