Question
Download Solution PDFThe cost of 21 pencils and 9 pens is Rs. 276, and the cost of 6 pencils and 3 pens is Rs. 84. The cost of 1 pencil and 1 pen is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Cost of 21 pencils and 9 pens = Rs. 276
Cost of 6 pencils and 3 pens = Rs. 84
Concept:
We need to form and solve a system of linear equations to find the individual cost of one pencil and one pen.
Calculation:
Let the cost of one pencil be x and the cost of one pen be y.
We have the equations:
⇒ 21x + 9y = 276 ...(1)
⇒ 6x + 3y = 84 ...(2)
Divide equation (2) by 3:
⇒ 2x + y = 28 ...(3)
Multiply equation (3) by 9:
⇒ 18x + 9y = 252 ...(4)
Subtract equation (4) from equation (1):
⇒ (21x + 9y) - (18x + 9y) = 276 - 252
⇒ 3x = 24
⇒ x = 8
Substitute x = 8 into equation (3):
⇒ 2(8) + y = 28
⇒ 16 + y = 28
⇒ y = 12
Hence, the cost of one pencil and one pen is:
⇒ x + y = 8 + 12
⇒ x + y = 20
∴ The cost of one pencil and one pen is Rs. 20.
Last updated on May 28, 2025
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