ratios and proportions

Question

Three numbers A, B and C are in the ratio of 12 : 15 : 25. If sum of these numbers is 312, find the ratio between the difference of B and A and the difference of C and B.  
(a) 3 : 7
(b) 10 : 3
(c) 3 : 10
(d) 7 : 3
(e) None of these

Answer 1

Let

$A=12 x$

$B = 15 x$

$C = 25 x$

 

Given that the Sum of A, B, and C = 312

$\implies 12 x + 15 x + 25 x = 312$

$\implies 32 x = 312$

$\implies x = 6$

Now,

$A = 12 x = 72$

$B=  15 x = 90$

$C = 25 x = 150$

Difference between B and A = 90- 72 = 18

Difference between C and B = 150 - 90 = 60

$\frac{Difference \ between\ B \ and \ A}{Difference \ between \ C \ and \ B }$ = $\frac{18}{60}=\frac{3}{10}$

 

Hence,Option $(C) 3 :10 .$

Answer 2

Option c