ICSE Class X Math 2013 Solved Paper

Question : 46 of 46

Marks: +1, -0

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.,

x-8

) then

\;\text " Number of books "\;=\;{960}/{x-8}

According to question,

\;{960}/{x-8}\;=\;{960}/{x}+4

\;{960}/{x-8}-\;{960}/{x}\;=4

960 [\;{x-x+8}/{x(x-8)}] \;=4

\;{8}/{x^2-8 x}\;=\;{1}/{240}

⇒ \;\; x^2-8 x\;=1,920

⇒ \;\; x^2-8 x-1,920\;=0

\;⇒ x^2-48 x+40 x-1,920=0

\;⇒ x(x-48)+40(x-48)=0

\;⇒ \;\; (x-48)(x+40)=0

\;x=48 \;\text " or "\; x=-40

∵ -40

is not possible.
Hence, the original cost of each book

=₹ 48

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