A man left ` 45,909 for his son and daughter who are 12 and 10 years old in such a way that if their shares be invested at 2% compound interest annually, they shall receive equal amount on reaching 15 years of age. How did he divide money ?
Answers
Given :- A man left Rs.45,909 for his son and daughter who are 12 and 10 years old in such a way that if their shares be invested at 2% compound interest annually, they shall receive equal amount on reaching 15 years of age.
To find :-
- How did he divide money ?
Solution :-
Let us assume that, the man gave Rs.x to younger son .
so,
→ Rs.x in 5 years = Rs.(45909 - x) in 3 years .
A/q,
→ x[1 + (2/100)]⁵ = (45909 - x)[1 + (2/100)]³
→ (45909 - x)/x = [1 + (2/100)]⁵ / [1 + (2/100)]³
→ (45909 - x)/x = [1 + (2/100)]²
→ (45909 - x)/x = (1 + 1/50)²
→ (45909 - x)/x = (51/50)²
→ (45909 - x)/x = 2601 / 2500
→ 2500 * 45909 - 2500x = 2601x
→ 2500 * 45909 = 2601x + 2500x
→ 2500 * 45909 = 5101x
→ x = (2500 * 45909)/5101
→ x = Rs.22500 .
therefore,
→ younger son gets = Rs.22500
→ Elder son gets = 45909 - 22500 = Rs.23409 .
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