Complex math

 David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A or 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?

A. Rs. 5000

B. Rs. 6500

C. 7500

D. None of these

E. Cannot be determined

Answer: Option A

Solution(By Myexaminer Team)

Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,

As we know:

Simple interest (S.I.) = principal amount (P) x interest rate (r) x time (t) /100

(x × 10 × 1/100) + (y × 12 × 1/100) + (z × 15 × 1/100) = 3200

= 10x + 12y + 15z = 320000 …(i)

Now, z = 240% of y = 12y/5 …(ii)

And, z = 150% of x =  3x/2 => x = 2/3 z = (2/3) × (12/5) × y  = 8y/5 …(iii)

From (i), (ii) and (iii), we have

16y + 12y + 36y = 320000 => 64y = 320000 => y = 5000

∴ Sum invested in Scheme B = Rs.5000