Multiple choice

Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is

  1. Rs. 759

  2. Rs. 792

  3. Rs. 818

  4. Rs. 828
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D Correct answer
Explanation

Let the parts be x, y, z. Amounts are x(1 + 0.05*2), y(1 + 0.05*3), z(1 + 0.05*4) = 1.1x = 1.15y = 1.2z. x:y:z = 1/1.1 : 1/1.15 : 1/1.2 = 1/110 : 1/115 : 1/120. Multiplying by common factors leads to the ratio 276:264:253. Sum = 793 parts. 2379 / 793 = 3. First part = 276 * 3 = 828.

AI explanation

Let the first part be x, so the amounts are x times 1.10, y times 1.15, and z times 1.20, where the total x plus y plus z is 2379. The ratios of the parts are the reciprocals of these multipliers, giving x is to y is to z as 1 divided by 1.10 is to 1 divided by 1.15 is to 1 divided by 1.20, which simplifies to 276 to 264 to 253. The total of these ratio units is 793, and multiplying the first ratio unit 276 by 3 gives the first part. Therefore, the first part is Rs. 828.

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