ICSE Class X Math 2013 Solved Paper

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Question : 46
Total: 46
A shopkeeper purchases a certain number of books for ₹ 960. If the cost per book was ₹ 8 less, the number of books that could be purchased for ₹ 960 would be 4 more. Write an equation, taking the original cost of each book to be x, and solve it to find the original cost of the books.
Solution:  
Given the original cost of each book be x.
Total cost =960 (Given)
Number of books for 960=
960
x

If the cost per book was 8 less, (i.e., x8 ) then
Number of books =
960
x8

According to question,
960
x8
=
960
x
+4

960
x8
960
x
=4

960[
xx+8
x(x8)
]
=4

8
x28x
=
1
240

x28x=1,920
x28x1,920=0
x248x+40x1,920=0
x(x48)+40(x48)=0
(x48)(x+40)=0
x=48 or x=40
40 is not possible.
Hence, the original cost of each book =48 .
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