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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.
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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