1) 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?
plzz do answer
Answers
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
So the cost of wheat is 22.5 Rs per K.G.
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
So the cost of wheat is 22.5 Rs per K.G.