A man invested Rs (P + 500) at the rate of 5% p.a. on simple interest for four years and received Rs 3000 as amount. If man invested Rs (2P +1000) at rate of ‘r’% p.a. on simple interest for three years and received Rs 1200, then find ‘r’?

Correct option is D

Information Given:

First investment: Rs (P + 500) at 5% simple interest for 4 years, amount received Rs 3000

Second investment: Rs (2P + 1000) at 'r'% simple interest for 3 years, amount received Rs 1200

Asked: Find value of 'r' (rate for second investment)

Formula Used:

Amount = Principal + Simple Interest

Simple Interest = (Principal × Rate × Time) / 100

Explanation:

For first investment, amount = Rs 3000

Amount = Principal + SI

Rs 3000 = (P + 500) + [(P + 500) × 5 × 4]/100

Rs 3000 = (P + 500) + (20(P + 500)/100)

Rs 3000 = (P + 500) + (P + 500)/5

Let (P + 500) = X

Rs 3000 = X + X/5 = (6X)/5

So, X = (3000 × 5)/6 = Rs 2500

Thus, P + 500 = Rs 2500

P = Rs 2000

For second investment, Principal = 2P + 1000 = (2 × 2000) + 1000 = Rs 5000

Amount received = Rs 1200

So, SI = Amount – Principal = Rs 1200 – Rs 5000 = [Negative], but since Rs 1200 is received that is only SI, so principal invested is Rs 5000.

SI = Principal × r × t /100 => 1200 = 5000 × r × 3 / 100

1200 = 15000r/100

1200 = 150r

r = 1200/150 = 8

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