Arithmetic

Simple & Compound Interest

Medium

The simple interest on a sum of Rs 1550 for 2 yrs is Rs 20 more than the simple interest on Rs 1450 for the same duration (the rate of interest is the same in both the cases). Find the rate of interest.

10%

15%

✅ Correct Option: 2

The first case involves Rs 1550 for 2 years, and the second case involves Rs 1450 for 2 years at the same rate. The interest on Rs 1550 is Rs 20 more than the interest on Rs 1450.

Simple Interest $= \dfrac{P \times R \times T}{100}$

For Rs 1550:

$SI_1 = \dfrac{1550 \times R \times 2}{100}$

For Rs 1450:

$SI_2 = \dfrac{1450 \times R \times 2}{100}$

The interest on Rs 1550 is Rs 20 more than the interest on Rs 1450:

$SI_1 = SI_2 + 20$

$\dfrac{1550 \times R \times 2}{100} = \dfrac{1450 \times R \times 2}{100} + 20$

$\dfrac{3100R}{100} = \dfrac{2900R}{100} + 20$

$\dfrac{3100R}{100} - \dfrac{2900R}{100} = 20$

$\dfrac{3100R - 2900R}{100} = 20$

$\dfrac{200R}{100} = 20$

$2R = 20$

$R = 10$

Therefore, the rate of interest is 10%.

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Solution

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