Question

A merchant buys 400 kg of wheat. She
sells two-fifths of the wheat at a profit
of 20%, one-fifth at a loss of 20% and
the remainder at a profit of 30%. If
she had sold the whole lot at a profit
of 25%, she would have gained 810
more. What is her cost price?​

Answer 1

Answer:

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Answer 2

AnsweR :-

The cost price of wheat is Rs 22.5 per KG.

SolutioN :-

Let the Cost Price (C. P.) of wheat is Rs x per K.G.

∴ Total cost price of 400 K.G. wheat = 400x

She sold ⅖ of wheat i.e. ( ⅖ × 400) = 160 K.G. at profit of 20%

∴ Selling price (s.p.) of 160 kg wheat = 160 (x + x × 20/100)

= 160 × ( x + x/5)

= 160 × 6x/5

= 192x

She sold ⅕ of wheat i.e. ( ⅕ × 400) = 80 K.G wheat at loss of 20%

∴ S. P. of 80 K.G. of wheat = 80 × {x - (x×20/100)}

= 80 × {x - x/5}

= 80 × 4x/5

= 64x

Remaining wheat = {400 - (160+80)} K.G.

= 400 - 240 K.G.

= 160 K.G.

∴ S. P. of remaining 160 K.G. wheat = 160 × { x + ( x × 30/100)}

= 160 × {x + 30x/100}

= 160 × ( x + 3x/10)

= 160 × 13x/10

= 208x

∴ Her profit on selling = Total S.P. - C.P.

= ( 192x + 64x + 208x) - 400x

= 464x - 400x

= 64x

If She sold total 400 K.G. wheat at a profit of 25% then S.P. of 400 K.G. wheat = 400 × { x + (x × 25/100)}

= 400 × {x + x/4}

= 400 × 5x/4

= 500x

∴ Her profit in that case = 500x - 400x

= 100x

By the Question ,

100x - 64x = 810

36x = 810

x = 810/36

$\huge{ \boxed { \sf{x = 22.5}}}$

So the cost of wheat is 22.5 Rs per K.G.