Online Mock Test - 2: Percentage And Fractions

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%).

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.

Explanation
Party D secured 12% more votes than Party R. Since Party R got 132,000 votes, Party D must have received 12% of 132,000, which is 15,840 votes more. Therefore, Party D received a total of 132,000 + 15,840 = 147,840 votes. The difference between the votes received by Party R and Party D is 147,840 - 132,000 = 15,840 votes. Hence, Party R lost the election by 15,840 votes.

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.

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.

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.

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.

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%.

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.

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.

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%.