16. A sum of Rs 44,200 is divided between John
and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10 % per annum compound interest, they will receive equal amounts on reaching 16 years of age.
(i) What is the share of each out of Rs 44,200 ?
(ii) What will each receive, when 16 years old ?
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Answers
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Step-by-step explanation:
(i) Let share of Jhon = Rs y
Share of Smith = Rs (44,200 - y)
Rate of interest = 10%
According to question
Amount of Jhon in 4 years = Amount of Smith in 2 years
⇒y(1+
100
10
)
4
−(44,200−y)(1+
100
10
)
2
⇒y(1+
100
10
)
2
=(44,200−y)
⇒y(
10
11
)
2
=(44,200−y)
⇒121y=100(44,200−y)
⇒121y=100×44,200−100y
⇒121y+100y=100×44,200
⇒221y=100×44,200
⇒y=
221
100×44,200
=Rs20,000
∴ Share of John = Rs 20,000
Share of Smith = Rs 44,200 - Rs 20,000
= Rs 24,200
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