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

A quicker route is to scale the total amount to the LCM of the two ratio sums so both shares come out as whole numbers straightaway.

Correct ratio $2:3:4$ has a sum of $9$ parts, and the wrong ratio $7:2:5$ has a sum of $14$ parts. Take the total amount as $126k$, where $126 = \text{LCM}(9,14)$, so it divides evenly under both ratios.

Correct B share $= \dfrac{3}{9}\times 126k = 42k$.

Wrong B share $= \dfrac{2}{14}\times 126k = 18k$.

The shortfall is $42k - 18k = 24k$, and this equals the given Rs 40, so $24k = 40$, giving $k = \dfrac{5}{3}$.

Total amount $= 126k = 126 \times \dfrac{5}{3} = 210$, confirming option A.

\[\boxed{Rs. \ 210}\]