vendor has 100 kg of vegetables. He sells a part of these at a gain 10% and the balance at a gain of 15%. If on the whole he earns a profit of 12%, the amount of vegetables sold at 10% gain is?
Answers
Given :- vendor has 100 kg of vegetables. He sells a part of these at a gain 10% and the balance at a gain of 15%. If on the whole he earns a profit of 12%, the amount of vegetables sold at 10% gain is ?
Solution :-
Let us assume that, the amount of vegetables sold at 10% gain is x kg and also Let us assume that, Price of 1 kg of vegetable is Rs.1.
So,
→ Price of 1 kg of vegetable = Rs.1
→ Price of x kg of vegetable = 1 * x = Rs.x
→ gain = 10% .
Than,
→ SP = CP * (100 + gain%) / 100
→ SP = x * (100 + 10)/100
→ SP = x * 110/100
→ SP of x kg of vegetables = Rs 1.1x .
Now, given that, vendor sold balance vegetables at 15% gain.
So,
→ Price of 1 kg of vegetable = Rs.1
→ Price of (100 - x) kg of vegetable = 1 * (100 - x) = Rs.(100 - x)
→ gain = 15% .
Than,
→ SP = CP * (100 + gain%) / 100
→ SP = {(100 - x) * (100 + 15)}/100
→ SP = (100 - x) * 115/100
→ SP of x kg of vegetables = Rs 1.15(100 - x) .
Also, given that, vendor total earns profit equal to 12% .
So,
→ Price of 1 kg of vegetable = Rs.1
→ Price of 100 kg of vegetable = 1 * 100 = Rs.100
→ gain = 12% .
Than,
→ SP = CP * (100 + gain%) / 100
→ SP = {100 * (100 + 12)}/100
→ SP = (100* 112)/100
→ SP of x kg of vegetables = Rs .112.
Therefore,
→ 1.1x + 1.15(100 - x) = 112
→ 1.1x - 1.15x + 115 = 112
→ 1.15x - 1.1x = 115 - 112
→ 0.05x = 3
→ (5/100)x = 3
→ 5x = 300
dividing both sides by 5,
→ x = 60 kg (Ans.)
Hence, the amount of vegetables sold at 10% gain is 60 kg.
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