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Asked in a 2000 paper

A, B, C and D divide a sum of money among themselves in the ratio 7:4:3:2. If D gets Rs. 500 less than A, find the total amount.

Correct answer: C. Rs.1600

  • A. Rs.100
  • B. Rs.700
  • C. Rs.1600
  • D. Rs.2000

Explanation

A and D differ by 7 − 2 = 5 ratio parts, and this difference is Rs.500, so one part is Rs.500 ÷ 5 = Rs.100. The total is 7 + 4 + 3 + 2 = 16 parts, giving 16 × Rs.100 = Rs.1600. The likely mistake is option d, Rs.2000, which uses an incorrect value for one ratio part.

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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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