Question : If a sum of Rs. 1,170 was distributed among A, B, and C in the ratio 2 : 3 : 4, by mistake, in place of $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$, who was benefited most and by how much?
Option 1: B, Rs. 220
Option 2: C, Rs. 250
Option 3: B, Rs.270
Option 4: A, Rs. 280
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Correct Answer: C, Rs. 250
Solution : The amount each person received when the sum was mistakenly distributed in the ratio = 2 : 3 : 4 The total parts in the ratio = 2 + 3 + 4 = 9 The amount each person should have received if the sum was correctly distributed in the ratio = $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ The amount each person should have received if the sum was correctly distributed in the ratio = 6 : 4 : 3 The total parts in the ratio = 6 + 4 + 3 = 13 On comparing the ratios, C benefited the most. Gain = $( \frac{4}{9}- \frac{3}{13}) \times1170$ Gain = Rs. 250 Hence, the correct answer is C, Rs. 250.
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