In what time will the simple interest on ₹2200 at 6% per annum be the same as that on ₹1650 at 9% per annum in 10 years? Option 1: 11 years and 3 months Option 2: 12 years Option 3: 12 years and 8 months Option 4: 11 years

Answer: 11 years and 3 months. Solution: We have two investments: - Investment A: ₹2200 at 6% per annum (time unknown) - Investment B: ₹1650 at 9% per annum for 10 years The simple interest on both investments must be equal. For Investment B (₹1650 at 9% for 10 years): Simple Interest = (Principal x Rate x Time)/100 SI = (1650 x 9 x 10)/100 SI = 148500/100 SI = ₹1485 For Investment A, the simple interest must also equal ₹1485. Given: - Principal = ₹2200 - Rate = 6% - Simple Interest = ₹1485 - Time = ? 1485 = (2200 x 6 x Time)/100 1485 = (13200 x Time)/100 1485 = 132 x Time Time = 1485/132 Time = 11.25 years Converting to years and months: 11.25 years = 11 years + 0.25 years 0.25 x 12 = 3 months Therefore, the time required is 11 years and 3 months.

Arithmetic

Simple & Compound Interest

Medium

In what time will the simple interest on ₹2200 at 6% per annum be the same as that on ₹1650 at 9% per annum in 10 years?

11 years and 3 months

12 years

12 years and 8 months

11 years

✅ Correct Option: 1

We have two investments:

Investment A: ₹2200 at 6% per annum (time unknown)
Investment B: ₹1650 at 9% per annum for 10 years

The simple interest on both investments must be equal.

For Investment B (₹1650 at 9% for 10 years):

Simple Interest $= \dfrac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$

$\text{SI} = \dfrac{1650 \times 9 \times 10}{100}$

$\text{SI} = \dfrac{148500}{100}$

$\text{SI} = ₹1485$

For Investment A, the simple interest must also equal ₹1485.

Given:

Principal = ₹2200
Rate = 6%
Simple Interest = ₹1485
Time = ?

$1485 = \dfrac{2200 \times 6 \times \text{Time}}{100}$

$1485 = \dfrac{13200 \times \text{Time}}{100}$

$1485 = 132 \times \text{Time}$

$\text{Time} = \dfrac{1485}{132}$

$\text{Time} = 11.25$ years

Converting to years and months:

$11.25$ years $= 11$ years $+ 0.25$ years

$0.25 \times 12 = 3$ months

Therefore, the time required is 11 years and 3 months.

2026: 14 May Shift 1

What is the least value of n (n is number of Years), the sum of money put out at 20% of CI (Compound Interest) will be more than double?

2026: 18 May Shift 1

The simple interest accrued on an amount of Rs. 84000 at the end of three years is Rs. 30240. What would be the compound interest accrued on the same amount at same rate in 2 years?

2026: 20 May Shift 1

The difference between compound interest and simple interest on a sum for 2 years at 20% per annum, when the interest is compounded annually is ₹32. If the interest were compounded half-yearly, the difference in two interests would be:

2026: 30 May Shift 2

Consider the simple interest of the following

(A) A sum of Rs 200 at 6% per annum for 5 yr.

(B) A sum of Rs 2000 at $13\frac{1}{2}$ % per annum for 4 yr.

(D) A sum of Rs 68000 at $16\frac{2}{3}$ % per annum for 9 months.

Arrange the above in descending order.

Choose the correct answer from the options given below:

2026: 31 May Shift 1

The difference between the amounts of compound interest and simple interest on the same amount invested at the same rate for 2 years in Rs. 32. If the interest rate is 4% per annum, calculate the amount invested.(in Rs.)

2026: 12 May Shift 1

Ravi invested at compound interest amounts to Rs 600 in 2nd year and 642 in 3 years. what rate of interest per annum he recevied ?

In what time will the simple interest on ₹2200 at 6% per annum be the same as that on ₹1650 at 9% per annum in 10 years?

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