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.