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29 Jul 2022, 20:56
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E
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Difficulty:
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60% (03:27) correct
40%
(02:44)
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A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will be
A. 18
B. 22
C. 26
D. 30
E. 34
Source : Wizako
A. 18
B. 22
C. 26
D. 30
E. 34
Source : Wizako
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29 Jul 2022, 22:34
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Suraj0184
A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will be
A. 18
B. 22
C. 26
D. 30
E. 34
Source : Wizako
A. 18
B. 22
C. 26
D. 30
E. 34
Source : Wizako
Let the cups sizes be Small, Medium, and Large
Let the price of a Small cup be 2x
Let the price of a Medium cup be 5x
Let the price of a Large cup be Ax
As per the information
2x * 5x * Ax = 800
After price increase
(2x + 6) * (5x + 6) * Ax = 3200
Dividing both these equations we get
10x^2 + 42x + 36 = 40x^2
=> 30x^2 - 42x - 36 = 0
=> 5x^2 - 7x - 6 = 0
=> 5x^2 - 10x + 3x - 6 = 0
=> 5x^2 - 10x + 3x - 6 = 0
=> 5x(x - 2) + 3(x - 2) = 0
=> (5x + 3)(x - 2) = 0
=> x = 2
Now
Small size = 4
Medium size = 10
Large = 20 (as the product is 800)
Sum of the original unit prices = 4+ 10 + 20 = 34
IMO Option E
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