The sum invested and simple interest earned on that sum are Rs. 75000 and Rs. 87750. Find the time for which the sum is invested if the rate was 15% for first some years and 18% for remaining 4 years.?

Question

The sum invested and simple interest earned on that sum are Rs. 75000 and Rs. 87750. Find the time for which the sum is invested if the rate was 15% for first some years and 18% for remaining 4 years.?

7 years
6 years
8 years
9 years

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 7 years

GIVEN:

Principal = Rs. 75000

SI = Rs. 87750

CONCEPT:

Simple interest concept.

Cumulative rate if the rate of interest is ‘R₁’ for ‘T₁’ years and ‘R₂’ for ‘T₂’ years = R₁T₁ + R₂T₂

FORMULA USED:

SI = PRT/100

Where P = Principal, R = rate of interest, T = Time

CALCULATION:

Suppose the rate was 15% for ‘t’ years.

So,

Cumulative rate = 15 × t + 18 × 4 = (15t + 72)%

Now,

/100 = 87750

⇒ (15t + 72) = 117

⇒ 15t = 45

⇒ t = 3

Hence,

Total time of investment = 3 + 4 = 7 years

∴ the time for which the sum is invested for the varying rate of Interest = 7 years.