The cost of 5 pens and 8 pencils is 120 while the cost of 8 pens and 5 pencils is Rs 153.Find the cost of 1 pen and that of 1 pencil.
Answers
Answered by
6
Answer:
Cost of pen =Rs.16
and cost of pencil =Rs.5
explanation
Let the cost of one pen is Rs.x and cost of one pencil is Rs.y, then
As per statement
5x+8y=120...(1)
8x+5y=153...(2)
Adding both the equations, we get
13x+13y=273
x+y=21....(3)
On subtracting (1) from (2),
3x−3y=33
x−y=11...(iv)
Again
Adding (3) and (iv).
2x=32 or x=16
On subtracting
2y=10 or y=5
Answered by
14
Given that:
- The cost of 5 pens and 8 pencils is 120.
- The cost of 8 pens and 5 pencils is Rs 153.
To Find:
- The cost of 1 pen and that of 1 pencil.
Let us assume:
- The cost of 1 pen = x
- The cost of 1 pencil = y
According to the question.
ㅤ↠ㅤ5x + 8y = 120 (i)
ㅤ↠ㅤ8x + 5y = 153 (ii)
Adding eqⁿ (i) & eqⁿ (ii).
ㅤ↠ㅤ13x + 13y = 273
ㅤ↠ㅤx + y = 21
Subtracting eqⁿ (ii) from eqⁿ (i).
ㅤ↠ㅤ-3x + 3y = - 33
ㅤ↠ㅤx - y = 11
Now,
ㅤ↠ㅤx - y = 11 (iii)
ㅤ↠ㅤx + y = 21 (iv)
Adding eqⁿ (iii) & eqⁿ (iv).
ㅤ↠ㅤ2x = (11 + 21)
ㅤ↠ㅤx = 32/2 = 16
Putting the value of x in eqⁿ (iv).
ㅤ↠ㅤ16 + y = 21
ㅤ↠ㅤy = 21 - 16
ㅤ↠ㅤy = 5
Hence,
- The cost of 1 pen = Rs. 16
- The cost of 1 pencil = Rs. 5
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