A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
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Answer:
Let the CP = 100x
So MP = 100x + 20% of 100x = 120x
Total SP = 5*120x + 15*0.9*120x + (35 – 15-3-5)*120x (1+p/100)
He is getting 15% in overall. So
35*100x *1.15 = 600x + 1620x + 1440x + 14.4px
4025 = 3660+14.4p
14.4p = 365
p = 365/14.4= 25.34
so p =25 (approx)
Let the price of Sugar per kilogram be 'x' rupees.
The man marks it up by 20% and sells 5 kilograms.
Marked Price = 1.2 × x = 1.2x
Therefore, the sale price of these 5 kgs totally would be = 5 × 1.2 × x = 6x
He then gives a discount of 10% on the markup and sells 15 kgs at that price. So, the price per kg now would be 0.9 × 1.2 × x = 1.08x
Therefore, the sale price of these 15 kgs totally would be = 15 × 1.08x = 16.2x
He then looses 3 kgs of Sugar
Therefore, the sale price of these 3 kgs = 0.
There is 35 - 5 - 15 - 3 = 12 kgs of sugar remaining.
Let's say it is sold at px price.
So, the sale price of these 12 kgs will be = 12 × px
The overall profit for the Man is 15%, So the Sale Price of the entire 35 kgs is 35 × 1.15 × x = 40.25x
Summing up and equating all the sale prices...
40.25x = 6x + 16.2x + 0x + 12 × px
40.25x = 22.2x + 12 × px
18.05x = 12 × px
Let's approximate this to
18x = 12 × px p = 3/2 = 1.5
Very importantly, px is attained after marking up the marked price.
Therefore, px = y × Marked Price
1.5x = y × 1.2x
y = 54 = 1.25
In other words we can say that the marked price was increased by 25%.
Answer
25