A producer of tea blends two varieties of tea from two tea gardens one costing Rs $18$ per kg and another Rs $20$ per kg in the ratio $x : y$ . If he sells the blended variety at Rs $21$ per kg. his gain percent is $12$ then the ratio is:

3 : 5

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3 : 4

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5 : 3

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1 : 1

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Solution

The correct option is C $5 : 3$
Ratio of two varieties of tea $= x : y$

Cost rate of first variety $= 18$ per kg and second variety $= 20$ per kg

Total cost (CP) $= \sum (a m o u n t \times P r i c e r a t e) = 18 x + 20 y$

Total selling price (SP) $= A m o u n t o f m i x t u r e \times R a t e o f m i x t u r e = (x + y) \times 21$

Given that Gain percentage $= 12 %$

$G a i n = S P - C P = (21 x + 21 y) - (18 x + 20 y) = 3 x + y$

Now, $G a i n p e r c e n t a g e = \frac{G a i n t i m e s 100}{C P} = \frac{(3 x + y) \times 100}{18 x + 20 y}$

$\Rightarrow 12 = \frac{(3 x + y) \times 100}{18 x + 20 y}$

$\Rightarrow 216 x + 240 y = 300 x + 100 y$

$\Rightarrow 140 y = 84 x$

$∴ \frac{x}{y} = \frac{140}{84} = \frac{5}{3}$

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A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio x:y. If he sells the blended variety at Rs 21 per kg. his gain percent is 12 then the ratio is:

A producer of tea blends two varieties of tea from two tea gardens one costing Rs $18$ per kg and another Rs $20$ per kg in the ratio $x : y$ . If he sells the blended variety at Rs $21$ per kg. his gain percent is $12$ then the ratio is: