Rs. 53 is divided among A, B, and C such that A gets Rs. 7 more than B, and B gets Rs. 8 more than C. What is the ratio A : B : C?

Introduction / Context:
When shares differ by fixed amounts, it’s efficient to set the smallest as a variable and express others relative to it. Then apply the total to find actual amounts and convert to a ratio.

Given Data / Assumptions:

• A = B + 7
• B = C + 8
• A + B + C = 53

Concept / Approach:
Let C = x ⇒ B = x + 8 ⇒ A = x + 15. Sum them to equal 53, solve for x, and then form the ratio from the actual amounts.

Step-by-Step Solution:
C = x, B = x + 8, A = x + 15Sum = (x + 15) + (x + 8) + x = 533x + 23 = 53 ⇒ 3x = 30 ⇒ x = 10Hence (A, B, C) = (25, 18, 10)Ratio A : B : C = 25 : 18 : 10

Verification / Alternative check:
Check differences: A − B = 7 and B − C = 8. Sum 25 + 18 + 10 = 53. All conditions satisfied.

Why Other Options Are Wrong:
They fail either the fixed-difference conditions or the total sum when examined.

Common Pitfalls:
Accidentally using 7 and 8 as ratios rather than differences; not preserving the order A, then B, then C when forming the ratio.

Final Answer:
25 : 18 : 10