Question

A certain amount was to be distributed among A, B and C in the ratio 2 : 3 : 4 respectively, but was erroneously distributed in the ratio 7 : 2 : 5 respectively. As a result of this, B got Rs.40 less. What is the amount?

• A. Rs. 210
• B. Rs. 270
• C. Rs. 230
• D. Rs. 280

Hint:

Write B's share under both ratios as a fraction of the same total, then equate their difference to Rs 40.

Answer 1

The Correct Option is A

Step 1: Write B's correct share as a fraction of the total.
Let the total amount be Rs \(x\).
Correct ratio is \(2:3:4\), so B's correct share \( = \dfrac{3}{2+3+4}x = \dfrac{3x}{9} = \dfrac{x}{3}\).

Step 2: Write B's actual (wrong) share as a fraction of the total.
Wrong ratio is \(7:2:5\), so B's actual share \( = \dfrac{2}{7+2+5}x = \dfrac{2x}{14} = \dfrac{x}{7}\).

Step 3: Set up the equation using the Rs 40 shortfall and solve.
Correct share \(-\) actual share \( = 40\)
\(\dfrac{x}{3} - \dfrac{x}{7} = 40 \Rightarrow \dfrac{7x - 3x}{21} = 40 \Rightarrow \dfrac{4x}{21} = 40 \Rightarrow x = \dfrac{40 \times 21}{4} = 210\).

Final Answer:
The total amount is Rs 210, so option A is correct. \[ \boxed{Rs. \ 210} \]