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Question
The cost of 5 pens and 8 pencils together cost Rs. 120 while 8 pens and 5 pencils together cost Rs. 153. Find the cost of a 1 pen and that of a 1pencil.
Solution
Let the cost of 1 pen and 1 pencil are ₹x and ₹y respectively.
Then as per the question
5x + 8y = 120 …….(i)
8x + 5y = 153 …….(ii)
Adding (i) and (ii), we get
13x + 13y = 273
⇒ x + y = 21 …….(iii)
Subtracting (i) from (ii), we get
3x – 3y = 33
⇒ x – y = 11 ………(iv)
Now, adding (iii) and (iv), we get
2x = 32 ⇒ x = 16
Substituting x = 16 in (iii), we have
16 + y = 21 ⇒ y = 5
Hence, the cost of 1 pen and 1 pencil are respectively ₹16 and ₹5.
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