Difficult Math Question #47 - Arithmetic

[800guy]

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%

[rajs.kumar]

Normal price = 3 x 15 + 2 x 18 = 81

After discount => 45x + 36y = 900

x + y = 22

Solving discount on pony (y) = 10%

[800guy]

here's the OA:

Ans : B

Total discount is 22% = $9

by back solving, in this case ,the discount percent for pony jeans should be less than 11% (22/2)because the price of this product is more.

take choice B
10% of 18= 1.8
total discount on 2 pony jeans= $3.6
22%-10%=12%
12% of 15 = $1.8
total discount on 3 fox jeans = $5.4
3fox jeans discount +2 pony jeans discount =$9
5.4 +3.6=9
so answer is B.

[nidhitanti]

[b]May be dumb question : but how do we get 900 in the total after discount below?[/b]

[quote="rajs.kumar"]Normal price = 3 x 15 + 2 x 18 = 81

After discount => 45x + 36y = 900

x + y = 22

Solving discount on pony (y) = 10%[/quote]

[roh00kan]

Nidhitanti,
the calculation goes like this:

3*15*x% + 2*18*y% = $9.00
45x/100 + 36y/100 = $9.00

45x + 36y = 9*100 ---> (1)
x + y = 22 ---> (2)

Statement 2* 45 = 45x + 45y = 22*45

Subtract statement 1 from this,

9y = 20*45+2*45-900 = 90

y = 90/9 = 10