Question

Q8. A sum of money amounts to Rs 14880 in 6 years and to Rs 16320 in 9 years. Find the sum of money and the rate of interest.

Answer 1

If the amount for a particular sum is Rs. 14880 in 6 years and Rs. 16320 in 9 years then the sum of money is Rs. 12000 and the rate of interest is 4% p.a.

Step-by-step explanation:

Required Formulas:

• Simple Interest = $\frac{PRT}{100}$

• Amount = Principal + Interest

Let the sum of money be Rs. “P” and the rate of interest be “R%”.

The amount after 6 years is given as Rs. 14880

The amount after 9 years is given as Rs. 16320

Based on the formulas above and the given data we can write the eq. as,

Equation 1:

A – P = PRT/100

⇒ 14880 – P = [PR*6]/100 …… (i)

Equation 2:

A – P = PRT/100

⇒ 16320 – P = [PR*9]/100 ……. (ii)

Now, dividing eq. (ii) by (i), we get

$\frac{16320 - P}{14880 - P} = \frac{\frac{PR*9}{100}}{\frac{PR*6}{100}}$

⇒ $\frac{16320 - P}{14880 - P} = \frac{9}{6}$

⇒ $\frac{16320 - P}{14880 - P} = \frac{3}{2}$

⇒ 2[16320 – P] = 3[14880 – P]

⇒ 32640 – 2P = 44640 – 3P

⇒ P = Rs. 12000

Substituting the value of P in eq. (i), we get

14880 – 12000 = $\frac{12000 * R * 6}{100}$

⇒ 2880 = 720 * R

⇒ R = $\frac{2880}{720}$

⇒ R = 4%

Thus, the sum of money is Rs. 12000 and the rate of interest is 4% p.a.

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