Concept of “Simple Interest”-08

Question: A man invests an amount of Rs. 15860 in the names of his three sons A, B, and C in such a way that they get the same amount after 2, 3 and 4 years respectively. If the rate of simple interest is 5% pan, then what is the difference between the amounts invested in the names of A and C? [Ans. (c) Rs. 460]

(a) Rs.480 (b) Rs.960 (c) Rs.460 (d) Rs.260 (e) none of these

Solution:

Detailed Explanation: Let x, y and z are respectively the three parts of the total investments of Rs.15860, that the man invested in the names of his three sons A, B and C. The simple interest rate is 5% pan. Given that the amount of the investments in the names of A, B and C made for 2, 3 and 4 years respectively are equal.

So, x +y + z = 15860

And also, 110% of x = 115% of y = 120% of z

Or, 22×x= 23×y = 24×z

Dividing throughout by 22×23×24, we get

x/(23×24) = y/(22×24) = z/(22×23)

Or, x/(23×12) = y/(11×24) = z/(11×23)

Or, x: y: z = 276: 264: 253

Now, 793 ≡ Rs.15860 [total investments]

1 ≡ Rs.20

23 ≡? = Rs.460 [difference between A (276) and C (253)]

Ans.