1. Ramesh invested Rs. 42,87,500 for future of his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 20 years. The original amount of Rs. 42,87,500 has been instructed to be invested at 10% p.a. simple interest. Find the amount invested by Ramesh for her elder daughter ?
Answers
Given : Ramesh invested Rs. 42,87,500 for future of his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 20 years
The original amount of Rs. 42,87,500 has been instructed to be invested at 10% p.a. simple interest.
To Find : the amount invested by Ramesh for her elder daughter
Solution:
Elder daughter will get interest for 5 years
and younger daughter will get interest for 10 years
Let say elder daughter investment = x
and younger daughters = 42,87,500 - x
elder daughter will get = x + x * 5 * 10 /100
= 1.5x
Younger daughter will get = (42,87,500 - x) ( 1 + 10 * 10/100)
= 2 (42,87,500 - x)
Equate both
=> 1.5x = 2 (42,87,500 - x)
=> x = 2 (42,87,500) / 3.5
=> x = 24,50,000
Hence elder daughter investment = 24,50,000 Rs
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Solution :-
Let us assume that, ramesh invested Rs.x for her elder daughter .
so, for elder daughter :-
→ Principal = P = Rs.x
→ Time = T= 20 - 15 = 5 years
→ Rate = 10% per annum .
then,
→ Amount recieved = P + SI = P + (P * R * T)/100 = x + {(x * 5 * 10)/100} = x + (x/2) = Rs.(3x/2)
and, for younger daughter :-
→ Principal = P = Rs.(4287500 - x)
→ Time = T= 20 - 10 = 10 years
→ Rate = 10% per annum .
then,
→ Amount recieved = P + SI = P + (P * R * T)/100 = (4287500 - x) + {(4287500 - x) * 10 * 10)/100} = (4287500 - x) + (4287500 - x) = Rs. 2(4287500 - x)
since both daughters gets same amount .
A/q,
→ 3x /2 = 2(4287500 - x)
→ 3x = 4 * 4287500 - 4x
→ 7x = 4 * 4287500
→ x = Rs.2450000 (Ans.)
Hence, the amount invested by ramesh for her elder daughter is Rs.2450000 .
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