Arithmetic

Simple & Compound Interest

Medium

A sum of ₹ 5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?

₹ 2300 and 3200

₹ 2700 and ₹ 2800

₹ 2500 and ₹ 3000

₹ 2400 and ₹ 3100

✅ Correct Option: 3

₹5500 is split into two parts. The interest earned on both parts is equal, with different interest rates (12% vs 8%) and different time periods (4 years vs 5 years).

Let the first part = $x$

Then the second part = $(5500 - x)$

Simple Interest Formula: SI = $\frac{P \times R \times T}{100}$

Interest on first part = $\frac{x \times 12 \times 4}{100}$

$= \frac{48x}{100}$

Interest on second part = $\frac{(5500-x) \times 8 \times 5}{100}$

$= \frac{(5500-x) \times 40}{100}$

Since both interests are equal:

$\frac{48x}{100} = \frac{(5500-x) \times 40}{100}$

$48x = (5500 - x) \times 40$

$48x = 220000 - 40x$

$48x + 40x = 220000$

$88x = 220000$

$x = \frac{220000}{88}$

$x = 2500$

First part = ₹2500

Second part = $5500 - 2500 =$ ₹3000

Therefore, the two parts of the sum are ₹2500 and ₹3000.

2024

A certain sum becomes ₹ 2,356 in 3 years and ₹ 2,660 in 5 years on simple interest. The value of sum is:

2025: 20 May Shift 1

Consider the compound interest of the following

(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522

(B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434

Choose the correct statement(s):

2023: 28 May Shift 1

If Rs 64 amounts to Rs 83.20 in 2 years on simple interest, then how much will Rs 86 amount to in 4 years at the same rate percent per annum ?

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:

2022: 17 Aug Shift 1

The interest earned on $\rupee 25000$ in 5 years at simple interest is $\rupee 1500$ . What is the rate of interest?

2023: 24 May Shift 3

For a certain period, simple interest on Rs. 1000 at 10% per annum is Rs. 100 more than that on Rs. 800. Find the period (in years).

A sum of ₹ 5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?

Solution

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