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
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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.
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Answer
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.
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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.
[ check your answer -
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]
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
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