Mohan invested certain sum in three different schemes P,Q and R with the rates of interest 10% per annum, 12% per annum and 15% per annum, respectively. If the total interest accrued in 1 yr was ₹ 3200 and the amount invested in scheme R was 150% of the amount invested in scheme P and 240% of the amount invested in scheme Q, what was the amount invested in scheme Q ?

Correct option is A

Given:

1. The total interest accrued in 1 year is ₹3200.

2. Scheme P's interest rate is 10% per annum.

3. Scheme Q's interest rate is 12% per annum.

4. Scheme R's interest rate is 15% per annum.

5. The amount invested in Scheme R is 150% of the amount invested in Scheme P.

6. The amount invested in Scheme R is 240% of the amount invested in Scheme Q.

Formula Used:

Simple Interest Formula:

I = (P * R * T) / 100

Where:

I = Interest, P = Principal (amount invested), R = Rate of interest, T = Time in years.

Solution:

Let the amount invested in Scheme Q be ₹ x.

According to the problem:

1. The amount invested in Scheme P = x / 2.4

2. The amount invested in Scheme R = 5x / 8

Now, the total interest from all three schemes is the sum of the interests from each scheme.

Interest from Scheme P:

Interest from Scheme P = ((x / 2.4) * 10 * 1) / 100 = x / 24

Interest from Scheme Q:

Interest from Scheme Q = (x * 12 * 1) / 100 = 12x / 100 = 3x / 25

Interest from Scheme R:

Interest from Scheme R = ((5x / 8) * 15 * 1) / 100 = 75x / 800 = 15x / 160

Sum of the interest:

(x / 24) + (3x / 25) + (15x / 160) = 3200

Find a common denominator (160):

(10x / 240) + (19x / 160) + (15x / 160) = 3200

(10x / 240) + (34x / 160) = 3200

Convert to a common denominator and solve for x:

(5x / 80) + (17x / 80) = 3200

(22x / 80) = 3200

x = (3200 * 80) / 22

x = ₹ 8000

Final Answer:

₹ 8000