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?
Solution
Correct Answer: Option A
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
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