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Question
9 pens and 5 pencils cost Rs.32, and 7 pens and 8 pencils cost Rs.29. Find the unit price for each pen and pencil.
Solution
Let the unit price for each pen = Rs. x
and the unit price for each pencil = Rs. y
According to given information, we have
9x + 5y = 32 ....(i)
7x + 8y = 29 ....(ii)
Multiplying eqn. (i) by 8 and eqn. (ii) by 5, we get
72x + 40y = 256 ....(iii)
35x + 40y = 145 ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
37x = 111
⇒ x = 3
⇒ 9(3) + 5y = 32
⇒ 27 + 5y = 32
⇒ 5y = 5
⇒ y = 1
Thus, the unit price for each pen is rs. 3 and that for each pencil is Rs.1.
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