Question

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity of sugar sold at 18% profit is
$
  {\text{A}}{\text{. }}560kg \\
  {\text{B}}{\text{. }}600kg \\
  {\text{C}}{\text{. }}400kg \\
  {\text{D}}{\text{. }}640kg \\
 $

Answer 1

Hint: Here we go through by first assuming the cost price of one kg for finding the overall profit and we have to also assume the amount of sugar that is sold on 8% gain and for 18% gain we will find by subtraction.

Complete step by step answer:
Here in the question it is given that a merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole.
Now first of all let the C.P. (cost price) of sugar be Rs. x per kg.
Then the C.P of 1000kg sugar is 1000x.
And now we have to assume that the sugar that is sold at 8% gain is y kg.
Then the sugar sold at 18% gain = (1000−y) kg.
Here in the first statement of question it says that he sells at a profit of 8%.
At first the C.P of y kg becomes Rs. xy
And we have to find the profit on y kg at the rate of 8%.
i.e. $xy + 8\% {\text{ of }}xy = xy + \left( {\dfrac{8}{{100}} \times xy} \right) = RS.\dfrac{{108xy}}{{100}}$
And the C.P of (1000-y) kg becomes Rs. (1000-y) x.
And similarly we have to find the profit on (1000-y) kg at the rate of 18%.
i.e. $x(1000 - y) + 18\% {\text{ of }}x(1000 - y) = x(1000 - y) + \left( {\dfrac{{18}}{{100}} \times x(1000 - y)} \right) = RS.\dfrac{{118x(1000 - y)}}{{100}}$
And the total profit that he earns on 1000kg of sugar is 14%.
i.e. $1000x + 14\% {\text{ of }}1000x = 1000x + \left( {\dfrac{{14}}{{100}} \times 1000x} \right) = RS.\dfrac{{114 \times 1000x}}{{100}}$
Now we equate it as,
Profit on sold by 8% + profit on sold by 18%= total profit
 $
   \Rightarrow RS.\dfrac{{108xy}}{{100}} + RS.\dfrac{{118x(1000 - y)}}{{100}} = RS.\dfrac{{114 \times 1000x}}{{100}} \\
   \Rightarrow \dfrac{{108y}}{{100}} + 1180 - \dfrac{{118y}}{{100}} = 1140 \\
   \Rightarrow \dfrac{{10y}}{{100}} = 40 \\
   \Rightarrow y = 400 \\
 $
$\therefore $ Quantity sold at 18% gain = (1000−400) kg=600kg

So, the correct answer is “Option B”.

Note: Whenever we face such a type of question the key concept for solving the question is to find the profit individually by assuming some parts as a variable then compare it with the total profits he made to find out the variables.