The sum of three numbers, namely, A, B and C, is 156. The numbers A and B are in the ratio of 2 : 5, while B and C are in the ratio of 1 : 9. Find number B?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15
Given:
- $A : B = 2 : 5$
- $B : C = 1 : 9$
- $A + B + C = 156$
Step 1: Make B common
From $A : B = 2 : 5$ → let
$A = 2x,\; B = 5x$
From $B : C = 1 : 9$ → let
$B = y,\; C = 9y$
To match B:
$5x = y$
Step 2: Express all in one variable
$A = 2x,\quad B = 5x,\quad C = 9(5x) = 45x$
Step 3: Use the sum
$2x + 5x + 45x = 156$
$52x = 156$
$x = 3$
Step 4: Find B
$B = 5x = 5 \times 3 = 15$
Correct Answer: 15