Question
Download Solution PDFThe cost of 3 pens and 5 pencils is Rs. 74. The cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by Rs. 34, What is the cost of 2 pens and 9 pencils?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The cost of 3 pens and 5 pencils is ₹74.
The cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by ₹34.
Calculations:
Let the cost of one pen be ₹x and the cost of one pencil be ₹y.
3x + 5y = 74 ....(i)
Cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by ₹34.
5x + 7y = 4x + 3y + 34
⇒ x + 4y = 34 ....(ii)
Now, solve equations (i) and (ii):
From (ii): x = 34 - 4y
Substitute x in (i):
3(34 - 4y) + 5y = 74
⇒ 102 - 12y + 5y = 74
⇒ 7y = 28 ⇒ y = 4
Substitute y in (ii):
x + 4(4) = 34 ⇒ x = 18
Now, we need the cost of 2 pens and 9 pencils:
2x + 9y = 2(18) + 9(4)
⇒ 2x + 9y = 36 + 36 = 72
∴ The correct answer is option (4).
Last updated on Apr 24, 2025
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