Question

Sandhya invested a certain amount in a bank. When the rate of interest changed from \( 10 \% \) to \( 121 / 2 \% \) her annual income increased by \( ₹ 1250 \). How much did Sandhya invest?

Answer 1

Let sandhya invest Rs. x.

∴ When r = 10%

total amount = x + 10x/100 = x + x/10 = 11x/10

When r = 12\(\frac12\)% = \(\frac{25}2\)%

Total amount = x + \(\cfrac{\frac{25}2x}{100}\) = x + \(\frac x8=\frac{9x}8\)

According to given condition, we have

\(\frac{9x}8-\frac{11x}{10}=1250\)

⇒ \(\frac{45x-44x}{40}=1250\)

⇒ x = 1250 x 40

 = 50000

Hence, sandhya invest Rs.50,000.