# 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 - Mathematics and Statistics

Sum

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.

Concept: Discount
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Commission, Brokerage and Discount
Exercise 1.2 | Q 5 | Page 11