A sells an article to B at a gain of 10% and B sells the same article to C at a gain of 12%.If C pays ₹616 for the article.Find how much did A pay for it.
Answers
Calculation of Initial Cost Price of article
Answer: Amount paid by A for article is Rs 500.
Explanation:
given that A sells an article to B at a gain of 10%
and B sells the same article to C at a gain of 12%.
C pays Rs 616 for the article
need to find how much A pay for it.
let assume amount paid by A for article = y
as A sells article to B at a gain of 10%
so amount paid by B = Amount paid by A + gain of 10%
=> amount paid by B = Amount paid by A + 10% of Amount paid by A
=> amount paid by B = y + 10% of y
=> amount paid by B = y + (10/100)×y = y + y/10
=> amount paid by B = 11y/10
As B sells same article to C at gain percent of 12
=> amount paid by C = Amount paid by B + gain of 12%
=> amount paid by C = Amount paid by B + 12% of Amount paid by B
As amount paid by B = 11y/10 ,
=> amount paid by C = 11y/10 + 12% of (11y/10)
=> amount paid by C = 11y/10 + (12/100) ×(11y/10)
=> amount paid by C = 11y/10 + (3/25) ×(11y/10)
=> amount paid by C = 11y/10 + 33y/250
=> amount paid by C = (275y +33y)/250 = 308y/250
=> amount paid by C = 308y/250
but its given amount paid by C = Rs 616
=> 308y/250 = 616
on solving above expression for y we get
y = (616 × 250) / 308
=>y = 2 x 250 = 500
Hence amount paid by A for article = y = Rs 500
There is also second method
amount paid by A = y
amount paid by B = y + 10% of y = y + (10/100)y = y ( 1 + 0.10) = 1.1y
amount paid by C = 1.1y + 12% of 1.1y = 1.1y + (12/100)×1.1y y = 1.1y + 0.12 × 1.1 y
=> amount paid by C = 1.1 y ( 1 + 0.12 ) [ taking 1.1y common ]
=> amount paid by C = 1.1 × 1.12 × y = 1.232y
=> 1.232y = 616
=>y = 616/1.232 = 500
Hence amount paid by A is Rs 500.
Any of the two methods can be used.
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