A man invested a total of Rs. 16,50,000 in the names of his two daughters aged 15 years and 17 years, respectively, such that they get equal amounts when they are 20 years old. If the rate of interest is 25% per annum, compounded annually, then how much money (in Rs., to the nearest tens) should be deposited in the name of his younger daughter?

Let the amount deposited for the younger daughter (aged 15) be P
1
​
and for the older daughter (aged 17) be P
2
​
.
Total investment: P
1
​
+P
2
​
=16,50,000

The younger daughter will earn interest for 20−15=5 years.
The older daughter will earn interest for 20−17=3 years.

Since they receive equal amounts at age 20:

P
1
​
(1+
100
25
​
)
5
=P
2
​
(1+
100
25
​
)
3

P
1
​
(1+
100
25
​
)
2
=P
2
​

P
1
​
(
4
5
​
)
2
=P
2
​

16
25
​
P
1
​
=P
2
​
⟹
P
2
​

P
1
​

​
=
25
16
​

The ratio of investment of younger daughter to older daughter is 16:25.
Sum of ratio terms = 16+25=41

Amount deposited for the younger daughter (P
1
​
):

P
1
​
=
41
16
​
×1650000
P
1
​
=
41
26400000
​
≈643902.43
Rounding off to the nearest tens gives Rs. 6,43,900.