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?

15

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