Joseph deposited a total of ₹52,500 in a bank in the names of his two daughters aged 15 years and 16 years in such a way that they would get equal amounts when they become 18 years old. If the bank gives 10% compound interest compounded annually, then what is the amount (in ₹) that Joseph had deposited in the name of his younger daughter?

25,000

Amount given to younger daughter = A

Amount given to elder daughter = ( 52500 - A )

Amount younger daughter get after 3 years   =  Amount elder daughter get after 2 years

A × ( 1 + \(\frac{rate }{100}\) )³  =   (52500-A) × ( 1 + \(\frac{rate }{100}\) )²

A × ( 1 + \(\frac{10 }{100}\) )³ =   (52500-A) × ( 1 + \(\frac{10 }{100}\) )²

A ×\(\frac{11 }{10}\)×\(\frac{11 }{10}\)×\(\frac{11 }{10}\) = ( 52500-A)×\(\frac{11 }{10}\)×\(\frac{11 }{10}\)

A ×\(\frac{11 }{10}\) = 52500 - A

\(\frac{11A }{10}\) + A = 52500

\(\frac{21A }{10}\) = 52500

A = Rs. 25000