A merchant has 2000 kg of sugar, part of which he sells at 16% profit and the rest at 36% profit. He gains 28% on the whole. The quantity sold at 36% profit is:Options :80010001200600
Question
A merchant has 2000 kg of sugar, part of which he sells at 16% profit and the rest at 36% profit. He gains 28% on the whole. The quantity sold at 36% profit is:Options :80010001200600
Solution
To solve this problem, we can use the concept of weighted average.
Let's denote:
- X as the quantity of sugar sold at 16% profit
- Y as the quantity of sugar sold at 36% profit
We know that X + Y = 2000 kg (total quantity of sugar)
The overall profit is 28%, so we can set up the following equation:
(X * 16% + Y * 36%) / 2000 = 28%
We can simplify this equation to:
0.16X + 0.36Y = 560
We now have a system of two equations:
- X + Y = 2000
- 0.16X + 0.36Y = 560
We can solve this system of equations to find the values of X and Y.
First, multiply the first equation by 0.16:
0.16X + 0.16Y = 320
Subtract this new equation from the second equation:
0.16X + 0.36Y - 0.16X - 0.16Y = 560 - 320 0.20Y = 240
Solve for Y:
Y = 240 / 0.20 = 1200 kg
So, the quantity of sugar sold at 36% profit is 1200 kg.
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