A student buys a certain number of books for rupees 40 less than 1000. If the cost of
each book was ₹ 8 less, the number of books that could be bought for ₹ 960 would
be 4 more. Taking the original cost of each book to be Rs.x, write and equation in x and solve it.
Answers
Information provided with us:
- Cost at which shopkeeper buys books = ₹960
- Cost of each book was ₹8 less
- The number of books that could be bought for ₹ 960 would be Rs.4 more
We have already assumed:
- Original cost of each book to be ₹.x
Finding out number of books for Rs.960:
- 960 would be divided with x to get number of books bought for ₹960
➝ 960/x
Thus number of books bought is 960/x
As cost of each book was ₹8 less:
Reducing the price,
➝ ₹(x-8)
Finding out number of books for Rs.960:
Here we are finding out the number of books by taking the reduced cost of each book.
That would be,
➝ 960/x-8
Subtracting both the prices which would be equal to 4:
Here we are subtracting both the prices of both the conditions that is, if the cost of
each book was ₹ 8 less and the number of books that could be bought for ₹ 960 would
be 4 more.
Thus, equation formed:
➝ (960/x-8) – (960/x) = 4
Taking L.CM.,
➝ 960x - 960x + 7680 / x(x-8) = 4
By cross multiplying we get,
➝ 960x - 960x + 7680 = 4(x² - 8x)
Now,
➝ 7680 = 4(x² - 8x)
Changing the sides,
➝ x² - 8x = 7680/4
On dividing we gets,
➝ x² - 8x = 1920