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Question
20 copies of a book can be purchased for a certain sum payable at the end of 6 months and 21 copies for the same sum in ready cash. Find the rate of interest.
Solution
Let the price of one book be ₹ x.
Now, 20 copies of the book are purchased for a certain sum due at the end of 6 months.
∴ P.W. of 20 books = 20x,
n = `6/12 = 1/2` years
Since, S.D. = P.W. + T.D.
∴ S.D. = P.W. + `(("P.W." xx "n" xx "r")/100)`
∴ S.D. = 20x + `(20 x xx 1/2 xx "r")/100`
∴ S.D. = `(2,000 x + 10x "r")/100`
Also, 21 copies of the book are purchased for the same sum but in ready cash.
∴ S.D. of 20 books = cost of 21 copies in ready cash
∴ `(2,000 x + 10 x "r")/100` = 21x
∴ `((2000 + 10"r")x)/100` = 21x
∴ `(2,000 + 10"r")/100` = 21
∴ 2,000 + 10r = 21 × 100
∴ 10r = 2,100 - 2,000
∴ 10r = 100
∴ r = `100/10`
∴ r = 10%
∴ Rate of interest is 10% p.a.
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