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Question
Ankita bought a gold ring worth Rs.x. The value of the ring increased at 10% per year compounded annually, on which the appreciation for the first year plus the appreciation for the second year amounts to Rs.6300. Find the value of the ring.
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Solution
Let the value of ring (P1) = Rs.100.
Appreciation (C.I.) for the 1st year
= Rs.`(100 xx 10 xx 1)/(100)`
= Rs.10
∴ Value of the ring at the end of 1st year (A1)
= Rs.100 + Rs.10
= Rs.110
∴ Value of the ring at the begging of 2nd year (P2) = Rs.110
Appreciation (C.I.) for the 2nd year
= Rs.`(110 xx 10 xx 1)/(100)`
= Rs.11
Sum of the appreciation (C.I.) for the 1st year and appreciation (C.I.) of 2nd year
= Rs.(10 + 11)
=Rs.21
Thus, when sum of appreciation is Rs.21, then value of the ring (P1) = Rs.100
And, when sum of appreciation is Rs.6300, then value of the ring
= Rs.`(100 xx 6300)/(21)`
= Rs.30000
So, the value of the ring is Rs.30000.
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