Online Mock Test - 2: Percentage and Fractions

1) A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

50

100

150

200

Let the maximum marks be x.
According to the given information, the passing marks would be 20% of x + 10, and the marks obtained by the second candidate would be 42% of x.
It is also mentioned that the second candidate gets 12% more than the passing marks, which means 42% of x is equal to 112% of (20% of x + 10).
Simplifying this equation, we get 42x/100 = 112(20x/100 + 10).
Solving this equation, we find that x = 100.

Explanation

Let the maximum marks be x.
According to the given information, the passing marks would be 20% of x + 10, and the marks obtained by the second candidate would be 42% of x.
It is also mentioned that the second candidate gets 12% more than the passing marks, which means 42% of x is equal to 112% of (20% of x + 10).
Simplifying this equation, we get 42x/100 = 112(20x/100 + 10).
Solving this equation, we find that x = 100.

2) 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?

10%

12%

8%

6.67%

If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, it means that he wants to limit his additional expenditure. To achieve this, he would have to reduce the quantity of petrol purchased by a certain percentage. To find this percentage, we can calculate the difference between the two increases and divide it by the original price increase. In this case, the difference is 10% (25% - 15%), and the original price increase is 25%. Therefore, Raj will reduce the quantity of petrol purchased by 8% (10% divided by 25%).

Explanation

If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, it means that he wants to limit his additional expenditure. To achieve this, he would have to reduce the quantity of petrol purchased by a certain percentage. To find this percentage, we can calculate the difference between the two increases and divide it by the original price increase. In this case, the difference is 10% (25% - 15%), and the original price increase is 25%. Therefore, Raj will reduce the quantity of petrol purchased by 8% (10% divided by 25%).

3) If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

25%

16.67%

20%

33.33%

If the price of petrol increases by 25%, the user's expenditure on petrol will also increase by the same percentage. In order to keep the expenditure constant, the user needs to cut down his consumption by the same percentage. Therefore, the user must cut down his consumption by 20% to maintain the same expenditure on petrol.

Explanation

If the price of petrol increases by 25%, the user's expenditure on petrol will also increase by the same percentage. In order to keep the expenditure constant, the user needs to cut down his consumption by the same percentage. Therefore, the user must cut down his consumption by 20% to maintain the same expenditure on petrol.

4) 40% of 70 is x% more than 30% of 80. Find x.

33.33%

40%

16.67%

25%

To find x, we need to compare 40% of 70 with 30% of 80. 40% of 70 is 28, and 30% of 80 is 24. Now we need to find the percentage difference between 28 and 24. To do this, we calculate (28 - 24)/24 * 100, which equals 16.67%. Therefore, x is 16.67%.

Explanation

To find x, we need to compare 40% of 70 with 30% of 80. 40% of 70 is 28, and 30% of 80 is 24. Now we need to find the percentage difference between 28 and 24. To do this, we calculate (28 - 24)/24 * 100, which equals 16.67%. Therefore, x is 16.67%.

5) 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?

35

250

75

85

Peter got 30% of the maximum marks and failed by 10 marks, while Paul got 40% of the total marks and got 15 marks more than the passing marks. This means that Peter's score is 10 marks below the passing marks, while Paul's score is 15 marks above the passing marks. Since Paul got 40% of the total marks, his score is 10 marks + 15 marks = 25 marks above Peter's score. Therefore, 25 marks represent a 10% difference in the total marks. To find the passing marks, we can calculate 10% of the total marks by dividing 25 marks by 10 and multiplying by 100, which gives us 250 marks. Therefore, the passing marks in the examination are 250.

Explanation

Peter got 30% of the maximum marks and failed by 10 marks, while Paul got 40% of the total marks and got 15 marks more than the passing marks. This means that Peter's score is 10 marks below the passing marks, while Paul's score is 15 marks above the passing marks. Since Paul got 40% of the total marks, his score is 10 marks + 15 marks = 25 marks above Peter's score. Therefore, 25 marks represent a 10% difference in the total marks. To find the passing marks, we can calculate 10% of the total marks by dividing 25 marks by 10 and multiplying by 100, which gives us 250 marks. Therefore, the passing marks in the examination are 250.

6) 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?

20% Profit

25% Loss

25% Profit

33.33% Loss

If the cost price of 20 articles is equal to the selling price of 16 articles, it means that the merchant is selling fewer articles for the same amount of money. This indicates that the selling price per article is higher than the cost price per article. To calculate the percentage of profit or loss, we need to find the difference between the selling price and the cost price, and then express it as a percentage of the cost price. In this case, since the selling price is higher than the cost price, it is a profit. The profit percentage can be calculated as (4/16) * 100 = 25%. Therefore, the merchant makes a 25% profit.

Explanation

If the cost price of 20 articles is equal to the selling price of 16 articles, it means that the merchant is selling fewer articles for the same amount of money. This indicates that the selling price per article is higher than the cost price per article. To calculate the percentage of profit or loss, we need to find the difference between the selling price and the cost price, and then express it as a percentage of the cost price. In this case, since the selling price is higher than the cost price, it is a profit. The profit percentage can be calculated as (4/16) * 100 = 25%. Therefore, the merchant makes a 25% profit.

7) 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?

17

23

77

None of these

The vendor sells 60% of the apples, which leaves him with 40% of the original amount. Then, he throws away 15% of the remaining 40%, which is equivalent to 6% of the original amount. Next, he sells 50% of the remaining 34% (40% - 6%), which is 17% of the original amount. Finally, he throws away the rest, which is the remaining 17% of the original amount. Therefore, the vendor throws away a total of 6% + 17% = 23% of his apples.

Explanation

The vendor sells 60% of the apples, which leaves him with 40% of the original amount. Then, he throws away 15% of the remaining 40%, which is equivalent to 6% of the original amount. Next, he sells 50% of the remaining 34% (40% - 6%), which is 17% of the original amount. Finally, he throws away the rest, which is the remaining 17% of the original amount. Therefore, the vendor throws away a total of 6% + 17% = 23% of his apples.

8) A shepherd has 1 million sheeps at the beginning of Year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheeps die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheeps. Which of the following is correct?

X > Y

Y > X

X = Y

Cannot be Determined

Since the population of sheep at the beginning of 2000 is 1 million and it decreases by y% during 2001, the number of sheep at the beginning of 2002 should be less than 1 million. However, the shepherd finds that he is left with 1 million sheep at the beginning of 2002. This implies that the percentage increase in the sheep population during the year 2000 (x%) must be greater than the percentage decrease in the sheep population during 2001 (y%). Therefore, X > Y.

Explanation

Since the population of sheep at the beginning of 2000 is 1 million and it decreases by y% during 2001, the number of sheep at the beginning of 2002 should be less than 1 million. However, the shepherd finds that he is left with 1 million sheep at the beginning of 2002. This implies that the percentage increase in the sheep population during the year 2000 (x%) must be greater than the percentage decrease in the sheep population during 2001 (y%). Therefore, X > Y.

9) 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?

15%

20%

80%

70%

The given information states that 20% of all men play football. Additionally, it is mentioned that 20% of men above the age of 50 play football. From this, we can infer that men above the age of 50 make up a portion of the football players. Since 80% of men are less than or equal to 50 years old, it is likely that a majority of the football players are in this age group. Therefore, the percentage of football players who are less than or equal to 50 years old is likely to be high, possibly around 80%.

Explanation

The given information states that 20% of all men play football. Additionally, it is mentioned that 20% of men above the age of 50 play football. From this, we can infer that men above the age of 50 make up a portion of the football players. Since 80% of men are less than or equal to 50 years old, it is likely that a majority of the football players are in this age group. Therefore, the percentage of football players who are less than or equal to 50 years old is likely to be high, possibly around 80%.

10) In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?

300,000

168,000

15,840

24,000

The question states that Party D received 12% more votes than Party R, which got 132,000 votes. To find the margin of loss, we calculate 12% of 132,000, which is 15,840. This represents the number of additional votes Party D received over Party R. Since elections are won by majority, Party D wins, and Party R loses by this 15,840 vote margin. This straightforward percentage comparison highlights the difference in support and is a direct way to measure election loss between two contenders.

Explanation

The question states that Party D received 12% more votes than Party R, which got 132,000 votes. To find the margin of loss, we calculate 12% of 132,000, which is 15,840. This represents the number of additional votes Party D received over Party R. Since elections are won by majority, Party D wins, and Party R loses by this 15,840 vote margin. This straightforward percentage comparison highlights the difference in support and is a direct way to measure election loss between two contenders.

11) 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?

1.5 kgs

1.7 kgs

3.33 kgs

None of these

To find out how much flower-nectar must be processed to yield 1kg of honey, we need to calculate the amount of water in both the nectar and the honey. The nectar contains 50% water, which means that for every 1kg of nectar, there is 0.5kg of water. The honey obtained from this nectar contains 15% water, which means that for every 1kg of honey, there is 0.15kg of water. To determine the amount of nectar needed to yield 1kg of honey, we can set up the equation: 1kg - 0.15kg = 0.5kg. Solving for the nectar weight, we get 0.5kg / 0.85kg = 1.7kg. Therefore, 1.7 kgs of flower-nectar must be processed to yield 1kg of honey.

Explanation

To find out how much flower-nectar must be processed to yield 1kg of honey, we need to calculate the amount of water in both the nectar and the honey. The nectar contains 50% water, which means that for every 1kg of nectar, there is 0.5kg of water. The honey obtained from this nectar contains 15% water, which means that for every 1kg of honey, there is 0.15kg of water. To determine the amount of nectar needed to yield 1kg of honey, we can set up the equation: 1kg - 0.15kg = 0.5kg. Solving for the nectar weight, we get 0.5kg / 0.85kg = 1.7kg. Therefore, 1.7 kgs of flower-nectar must be processed to yield 1kg of honey.