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A man invested Rs. P in scheme A on compound interest at rate of 10% p.a. for two years and he invested Rs. (P+500) in scheme B on simple interest at
Question


A man invested Rs. P in scheme A on compound interest at rate of 10% p.a. for two years and he invested Rs. (P+500) in scheme B on simple interest at rate of 12% p.a. for same period of time. If the interest received by man from scheme A is Rs. 150 less than that of from scheme B, then find amount invested in scheme B.

A.

1250 Rs.

B.

1000 Rs.

C.

1500 Rs.

D.

2000 Rs.

E.

2500 Rs.

Correct option is C


Information Given:
Amount invested in scheme A = Rs. P
Rate of compound interest in scheme A = 10% per annum
Time = 2 years
Amount invested in scheme B = Rs. (P + 500)
Rate of simple interest in scheme B = 12% per annum
Time = 2 years
Interest from scheme A is Rs. 150 less than interest from scheme B.
Concept/Formula Used:
Compound Interest for 2 years = CI=P×[(1+R100)21]\text{CI} = P \times \left[\left(1 + \frac{R}{100}\right)^2 - 1\right]​​
Simple Interest = P×R×T100\frac{P \times R \times T}{100}​​
Explanation:
Interest from scheme A:
CI=P×[(1+10100)21]\text{CI} = P \times \left[\left(1 + \frac{10}{100}\right)^2 - 1\right]​​
= P × (1.21 − 1)
= 0.21P
Interest from scheme B:
SI =(P+500)×12×2100\frac{(P + 500) \times 12 \times 2}{100}​​
= 0.24(P + 500)
According to the question:
0.24(P + 500) − 0.21P = 150
0.24P + 120 − 0.21P = 150
0.03P = 30
P = 1000
Amount invested in scheme B:
P + 500 = 1000 + 500 = 1500
Final Answer:
Amount invested in scheme B = Rs. 1500
Exam Hall Approach

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