Latest Maths Olympiad Aptitude Question SOLUTION: By receiving two successive discounts, a dealer bought merchandise for $9 that was listed at $20. What were the discounts in percent if the first discount was 5 times the second

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(#M40034350) MATHS OLYMPIAD question Keep an EYE

By receiving two successive discounts, a dealer bought merchandise for $9 that was listed at $20. What were the discounts in percent if the first discount was 5 times the second?

Asked In Maths Olympiad (10 years ago)

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Ann Theressa  (10 years ago)

50% and 10%

Let the discounts be 5x and x ( given the first discount was 5 times the 2nd)

1st discount = 20*5x/100 = x
price after discount = (20-x)

2nd discount = (20-x)*x/100
price after discount = (20-x) - [(20-x)*x/100]
given price after discount = 9
so,
(20-x) - [(20-x)*x/100] = 9
100*(20-x) - (20-x)*x =900
2000 - 100x -20x +x^2 = 900
x^2 - 120x + 1100 = 0
x^2 - 10x -110x + 1100 = 0
x(x-10) -110(x-10) = 0
(x-10)(x-110) = 0
===> x = 10 or 110
so discounts are 5*10=50% and 10%

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