Question:

A boy bought some books for Rs 60. If he had bought 5 more books for the same amount each book have cost Re. 1 less, find the number of books bought by the boy.

Posted by: Jenish s. on 23.09.2019

Let no. Of books bought be x, then cost of each book = 60/x. Now if he buy x+5 books , then cost of each book will be 60/(x +5). According to the question 60/x - 60/(x+5) =1. Now solve this equation. You will get the answer 15.

Let the number of books bought for Rs.60 were x,

Hence cost of 1 book is 60/x

Now if he bought x+5 books for Rs. 60 then cost of each book would have been Re. 1 less,

So , According to problem,

60/x -60/(x+5) = 1

Solving this we get x =15 , -20. So x =15 is the actual number of books since -20 is not possible.

Let the number of books be x

Price of x books = Rs 60

thus, price of 1 book = Rs 60/x ................. (i)

Now, new number of books = x + 5

Price = Rs 60

Hence, price of each book = Rs 60/(x + 5) ....................... (ii)

Now, 60/(x + 5) + 1 = 60/x

or, 60[1/x - 1/(x + 5)] = 1

or, 60[x + 5 - x]/x(x + 5) = 1

or, 300/x(x + 5) = 1

or, x(x + 5) = 300

or, x^2 + 5x - 300 = 0

or, x^2 + 20x - 15x - 300 = 0

or, x(x + 20) - 15(x + 20) = 0

or, (x + 20)(x - 15) = 0

or, x = 15, - 20

Hence, the original number of books were 15.

Let, the no. of books be x.

So, each book costs Rs. 60/x.

BTP, (x + 5)(60/x - 1) = 60 .

=> 60 - x + 300/x - 5 = 60   => x^2 + 5x - 300 = 0 .

Solving the eqn, we get, x = -20 or x = 15 .

Since, no. of books can't be -ve, the only possible value is 15 .

Let the number of books bought by the boy be x and the cost per book be y.

According to the given statement in the problem, xy=60

Also, given that, (y-1)(x+5)=60

By simplifying, we get xy-x+5y=65

But, we know that xy=60, we can also write it as x=60/y

Writing the equation in terms of y, we get y2-y-12=0

Solving it for y, we get y=4

Replacing y=4 in xy=60, we get x=15.

Therefore, the number of books bought by the boy=15.

Let the original cost of one book         =  Rs x

Then no.of books purchased                = 60/x

The new cost of one book                    =Rs (x-1)

No.of books purchased at this price   = 60/(x-1)

It is given that the number of books that could be purchased at the

new price is 5 more than at the original price.

Therefore 60/(x-1) - 60/x           =  5

That is   {60x - 60(x-1)}/{x(x-1)}   = 5

or 60/{x(x-1)}   =       5

that is 12/{x(x-1)}= 1 or x(x-1)= 12

The 2 factors of 12 in which one factor is 1 more than the other

are  4,3   or 4*3=12

Hence original cost of the book=  x         = Rs 4

The number of books purchased= 60/4=15.

Let total number of books be x

Cost of each book = Rs 60/x

Now if 5 more books had been purchsed i.e.  x+5 books had been purchased, then each book would have cost Rs 60/(x+5+) and this would have given a saving of Re 1 on each book.

So, 60/x - 60/(x+5) =1

Solving this we get, 60 x + 60 . 5 - 60x = 1 . x (x+5)

i.e. 300 = x^2 + 5x   or, x^2+5x - 300 =0

or, x^2+ 20x - 15x- 300 =0  [ by factorising LHS]

or, x(x+20)- 15 (x+20) = 0

or, (x+20) (x-15) = 0

or, x= -20 or x=15

x being total number of book can not be negative. so x=15.

Total number of book is  15.  ANS.

If 15 books are purchases, cost of each book = 60/15 = Rs 4.

If 5 more books i.e. 20 books had been purchased for same cost, each book would haave cost

60/20 = Rs 3 which is 1 less thas 4. Theanswer satifies condition of question]

Let no. of book be x and cost of each book be Rs. y so x.y= 60 now 5 more book is x+5 cost Rs. 1 less is y-1 so( x+5)(y-1) = 60 now solve equation 2 and put value of x.y and put y=60/x then you find x=15 so no of book is 15

Total amount = Rs 60.

Let the number of books bought initially = x

thus, price per book = Rs (60/x)

Now, if five more books were bought for Rs 60,

price of each book = Rs (60/x + 5)

now, 60/x - 60/(x + 5) = 1

or, 60[1/x - 1/(x + 5)] = 1

or, 60[x + 5 - x] = x(x + 5)

or, 300 = x^2 + 5x

or, x^2 + 5x - 300 = 0

or, x^2 + 20x - 15x - 300 = 0

or, x(x + 20) - 15(x + 20) = 0

or, (x + 20)(x - 15) = 0

thus, x = 15

Let number of books bought by the boy be X. Then average cost is 60/X. And average cost for (X+5) books is 60/(X+5), which is given to be 1 less than 60/X. Hence 60/(X+5) = 60/X - 1. Note that X & X+5 must be positive factors of 60 with 60/X - 60/(X+5) = 1. Thus only possible value of X is 15, since 60/15 - 60/20 = 4 - 3 = 1

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