Questions along with illustrative explanations
Question:
When processing flower-nectar into honeybees’ extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?
(1) 1.5 kgs
(2) 1.7 kgs
(3) 3.33 kgs
(4) None of these
Correct Answer - (2)
Solution:
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 85% (100-15).
Therefore 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg
Therefore amount of flower-nectar needed = (0.85/0.5) * 1kg = 1.7 kg.
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Question:
A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
(1) 17
(2) 23
(3) 77
(4) None of these
Correct Answer - (2)
Solution:
Let the number of apples be 100.
On the first day he sells 60% apples ie.,60 apples.Remaining apples =40.
He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40-6 = 34 apples
The next day he throws 50% of the remaining 34 apples i.e., 17.
Therefore in all he throws 6+17 =23 apples.
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Question:
If the cost price of 20 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
(1) 20% Profit
(2) 25% Loss
(3) 25% Profit
(4) 33.33% Loss
Correct Answer - (3)
Solution:
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 20 articles = Rs. 20.
Selling price of 16 articles = Rs. 20
Therefore, Selling price of 20 articles = (20/16) * 20 = 25
Profit = Selling price - Cost price
= 25 - 20 = 5
Percentage of profit = Profit / Cost price * 100.
= 5 / 20 * 100 = 25% Profit
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Question:
Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?
(1) 35
(2) 250
(3) 75
(4) 85
Correct Answer - (4)
Solution:
Let ‘x’ be the maximum marks in the examination.
Therefore, Peter got 30% of x = 0.3x
And Paul got 40% of x = = 0.4x.
In terms of the maximum marks Paul got 0.4x - 0.3x = 0.1x more than Peter. —— (1)
The problem however, states that Paul got 15 marks more than the passing mark and Peter got 10 marks less than the passing mark.
Therefore, Paul has got 15 + 10 = 25 marks more than Peter. —— (2)
Equating (1) and (2), we get
0.1x = 25 => x = 250
‘x’ is the maximum mark and is equal to 250 marks.
We know that Peter got 30% of the maximum marks. Therefore, Peter got = 75 marks.
We also know that Peter got 10 marks less than the passing mark. Therefore, the passing mark will be 10 marks more than what Peter got = 75 + 10 = 85.
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Question:
If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
1. 10%
2. 12%
3. 8%
4. 6.67%
Correct Answer - 8%. Choice (3)
Solution:
Let the price of 1 litre of petrol be Rs.x and let Raj initially buy ‘y’ litres of petrol.
Therefore, he would have spent Rs. xy on petrol.
When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.
Raj intends to increase the amount he spends on petrol by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy
Let the new quantity of petrol that he can get be ‘q’.
Then, 1.25x * q = 1.15xy
Or q = 0.92y.
As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.
Or a reduction of 8%.
