Thursday, 24 March 2016

Aptitude Questions for Bank Tests - Ratio and Proportion Solved Problems 1

Quantitative Aptitude Questions – Ratio and Proportion


1.    Find the fourth proportional to the numbers 8,12 and 16
Explanation: The fourth proportion of a,b and c is
bc / a
    Therefore, fourth proportional of 8,12 and 16 =
12 x 16 / 8
= 24

2.    What is the third proportional to 18, 12?
Explnation: Third proportion of a and b is
b2 / a
           Third proportion of 18 and 12 =
122 / 18
= 8

3.    What is the mean proportional between 16 and 25 ?
Explnation: The mean proportional of a and b is  a x b 
 mean proportion of 16 and 25 is =  16 x 25  =  400 = 20

4.    If A:B = 3:1 and B:C = 2:3 . What is the value of A:B:C?
Explnation:   In the given 2 ratios, the common term is B. To write the two ratios into a single ratio, the values of the common term must be equal.
A : B : C                 A : B : C                
               3  : 1       x  2        6 : 2
                     2: 3                      2 : 3   
                                             6 : 2 : 3

5.    If A:B=2:5   , B:C = 5:4  and C:D = 6:1. Then what is the value of A : D ?
Explanation: 
A / B
x
B / C
x
C / D
=
A / D
 A:D =
2 / 5
x
5 / 4
x
6 / 1
=
3 / 1
= 3:1

6.    Rs 3798 is divided into parts in the ratio of  5:4. What is the value of the 1st part?
Explanation:: Divided in the ratio= 5:4   
      Sum of the parts= 5+4= 9
1st part = Rs 3798 = $\frac{5}{9}$ = Rs 2110

7.    A sum of money is divided between A and B in the ratio of 11:3 . The difference between their shares is Rs 6400. Find the total amount?
Explanation:  : Let A and B got 11x and 3x .
The difference between their shares 11x – 3x = 8x =6400 =>x = 800
 Total amount= Sum of the shares = 11x + 3x
=> 14x = 14 x 800 =Rs 11200

8.    The sum of the two numbers is 72. Which of the following cannot be the ratio of those two numbers ?
a)8:1       b ) 5:3          c)11:7           d)7:3
Explanation: The sum of the numbers is 72.
The sum of the terms of the ratio must divide the sum of the numbers.
Taking option 1 : Sum of the terms = 8+1 = 9 which divides 72.
Taking option 2 : Sum of the terams = 5 +3 = 8 which divides 72.
Taking option 3: Sum of the terms = 11 +7 = 18 which divides 72
Taking option 4: Sum of the terms = 7+3 = 10 which is not factor of 72.
 So this cannot the  required ratio.

9.    The price of a TV and a Radio are in the ratio of 7:2. If a T.V. costs 25000 more than a Radio, find the price of the T.V.?
Explanation : When TV costs more than the radio by Rs 25000 means , the difference between the price of T.V. and Radio is Rs 25000
Prices of TV and Radio are in the ratio 7:2. Let their prices be 7x and 2x.
The difference of their prices => 7x-2x => 5x = Rs 25000=> x= Rs 5000
The price of the TV => 7x = 7 x 5000 = Rs 35000

10. Rs 2400 is divided among A, B and C . Half of the A’s share , $\frac{1}{3}$ of the B’s share and $\frac{1}{5}$ th of the C’s share are equal. Then find the share of C?
Explanation:
1 / 2
A =
1 / 3
B =
1 / 5
C are equal. 

     We say they are equal to k
            
1 / 2
A =
1 / 3
B =
1 / 5
C= k
         Therefore A=2k B= 3k and C=5k.
The ratio of the shares of A,B and C = 2k :3k: 5K= 2:3:5
         The share of C = Rs 2400 x
5 / 10
  = Rs 1200

11. Rs 3720 is divided into three parts in proportional to the fractions $\frac{1}{2}$ : $\frac{1}{3}$: $\frac{1}{5}$ . What is the second part?
Explanation:        
1 / 2
:
1 / 3
:
1 / 5
=
15 / 30
:
10 / 30
:
6 / 30
         The required ratio = 15: 10:6
        second part = Rs 3720 x
10 / 31
=Rs 1200

12. Two numbers are in the ratio of 4:5 and their product is 500.Find the bigger number?
Explanation: Let two numbers be 4x and 5x.
 Product of the numbers =>4x x 5x => 20x2 = 500
                                  => x2 = 25 =>x=5
        Bigger number = 5x= 5 x 5 = 25    
                                                                                             
13. Rs 3120 is divided among A,B and C so that 3 times the A’s share, and twice the B’s share and 4 times of the C’s share are equal. Find the share of A ?
Explanation:
3 times the A’s share, and twice the B’s share and 4 times of the C’s share are equal 3A = 2B= 4C = k
A =
k / 3
, B=
k / 2
  C=
k / 4
  => A:B:C =
k / 3
:
k / 2
:
k / 4
                                        A: B : C =  
4:6:3 / 12
    
The required ratio = 4:6:3
  Share of A = Rs 3120 x
4 / 13
= Rs 960

14. Rs 7820 are divided among A, B and C so that A receives $\frac{5}{12}$ as much as B and C together receive and B receives $\frac{1}{3}$ as much as A and C together receive. Find the difference between the shares of A and B ?
Explanation : A receives
4 / 13
as much as B and C together receive.
           A =
5 / 12
(B+C)=> A : (B+C)= 5:12
    A’s share = Rs 7820 x
5 / 17
=Rs 2300
B receives
4 / 13
as much as A and C together receive
   B =
4 / 13
(A+C)=> B: (A+C)= 4:13
        B’s share = Rs 7820 x
4 / 17
= Rs 1840
Difference between A and B’s share = Rs 2300 –Rs 1840 =Rs 46013.                                                     
15. 
Three numbers are in the ratio 5:4:3 such that the sum of their squares is 0. What is the smallest number?
Explanation: The numbers are in the ratio of 5:4:3.
Let numbers be 5x,4x and 3x. Given that sum of their squares is 450
Sum of their squares = (5x)2+(4x)2+(3x)2
ð  25x2 + 16 x2 + 9 x2 = 450
ð  50 x2 =450
ð  x2=9
ð  x=3
    Smallest number = 3x = 3 x 3 =9