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If a number of pens and pencil are bought in the ratio of 5:3, Ashok has to pay Rs44.If the ratio is changed as 3:5,then he has to
pay Rs36.Find the ratio of the price of one pen to one pencil.
5:3
7:3
8:5
7:4
To solve this problem, we need to find the price ratio of one pen to one pencil.
- Let's denote the price of a pen as "p" and the price of a pencil as "q".
- Initially, pens and pencils are bought in the ratio 5:3 for Rs 44.
- This means: 5p + 3q = 44.
- Later, they are bought in the ratio 3:5 for Rs 36.
- This means: 3p + 5q = 36.
- Now, solve these two equations simultaneously to find the ratio of p to q.
Solving the Equations:
Multiply the first equation (5p + 3q = 44) by 5:
25p+15q=220
Multiply the second equation (3p + 5q = 36) by 3:
9p+15q=108
Subtract the second equation from the first:
16p=112
p=7
Substitute p = 7 back into one of the original equations to find q. Using 3p + 5q = 36:
3(7)+5q=36
21+5q=36
5q=15
q=3
Therefore, the ratio of the price of one pen (p) to one pencil (q) is 7:3.
Correct Answer: Option 2, 7:3
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