- QUESTION
Given below are two statements:
Statement!:
In order to get a mixture worth 16-5/kg, a grocer needs to mix two varieties of pulses costing 15 and 20 per kg respectively in the ratio 7:3.
Statement II:
A merchant has 1000 kg rice, part of which he sells at 8% profit and the rest at
16% profit. He gains 14% on the whole. The quantity of rice sold at 16% profit is 750 kg. In the light of the above statements,
choose the correct answer from the option given below:
A)Both Statement I and Statement il are true
B)Both Statement I and Statement II are false
C)Statement I is true but Statement II is false
D)Statement I is false but Statement II is true
Explanation
(A)
=Let’s evaluate each statement:
Statement I:
The grocer needs to mix two varieties of pulses costing 15 and 20 per kg respectively in the ratio 7:3 to get a mixture worth 16.5/kg.
Let’s denote the quantities of the two varieties as 7x and 3x, where x is a common multiplier.
According to the given conditions:
Total cost of the mixture = (Cost of 1st variety * Quantity of 1st variety) + (Cost of 2nd variety * Quantity of 2nd variety)
16.5 = (15 * 7x) + (20 * 3x)
16.5 = (105x + 60x)
16.5 = 165x
x = 1/10
So, the quantities of the two varieties are 7/10 kg and 3/10 kg respectively.
Statement I is true.
Statement II:
A merchant has 1000 kg rice, part of which he sells at 8% profit and the rest at 16% profit. He gains 14% on the whole. The quantity of rice sold at 16% profit is 750 kg.
Let’s denote the quantity of rice sold at 8% profit as x kg. Then, the quantity sold at 16% profit would be (1000 – x) kg.
According to the given conditions:
Total profit = (Profit on 8% portion) + (Profit on 16% portion)
14% of 1000 = (8% of x) + (16% of (1000 – x))
140 = (0.08x) + (0.16(1000 – x))
140 = 0.08x + 160 – 0.16x
140 = 160 – 0.08x
-20 = -0.08x
x = 250
So, the quantity of rice sold at 8% profit is 250 kg and at 16% profit is (1000 – 250) = 750 kg.
Statement II is true.
Therefore, the correct answer is (1) Both Statement I and Statement II are true.
Question – 2
A dishonest dealer sells his goods at 10% loss on cost price and uses 30% less weight. What is his profit or loss percentage?
A)28 4/7 % loss
B)28 3/7 % profit
C)28 3/7 % loss
D)28 4/7 % profit
Explanation
(D)
=28 4/7 % profit
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