Aptitude : Percentage

(6) In an election between two candidates, one got 55% of the total valid votes. If the total votes were 6000, find the number of votes the other candidate got.

• (a)2500 votes
• (b)2700 votes
• (c)2400 votes
• (d)2800 votes

Answer

Correct Answer : (b) 2700 votes
If one candidate got 55% of the total valid votes, then the other candidate got 45% of the total valid votes.
Hence, the number of votes the other candidate got = 45/100 * 6000 = 2700 votes.

(7) If the price of a book increases by 15%, by what percentage should a person reduce consumption so that the expenditure remains the same?

• (a)13.04 Percentage
• (b)13.5 Percentage
• (c)14.15 Percentage
• (d)15 Percentage

Answer

Correct Answer : (a) 13.04 Percentage
Let’s assume the initial price of the book was P and the initial quantity demanded was Q. After the price increase of 15%, the new price becomes P + 0.15P = 1.15P.
Now, we need to find the percentage reduction in quantity demanded that compensates for the price increase, such that the expenditure remains the same.
The expenditure on the book can be calculated as the product of the price and the quantity demanded:
Initial Expenditure = P * Q
New Expenditure = (1.15P) * (Q – R)
where R represents the reduction in quantity demanded.
Since the expenditure remains the same, we have:
Initial Expenditure = New Expenditure
P * Q = (1.15P) * (Q – R)
Simplifying the equation:
Q = 1.15Q – 1.15R
1.15R = 0.15Q
R = (0.15Q) / 1.15
R ? 0.1304Q
Therefore, a person should reduce their consumption by approximately 13.04% (rounded to two decimal places) to maintain the same expenditure after a 15% increase in the price of the book.

(8) A fruit seller sells mangoes at 20% profit. If he bought it at 10% less and sold it at Rs. 110 per kg, what is the cost price?

• (a)72.5 Rupees per KG
• (b)80.5 Rupees per KG
• (c)85.5 Rupees per KG
• (d)82.5 Rupees per KG

Answer

Correct Answer : (d) 82.5 Rupees per KG
To calculate this, we first need to figure out the original cost price before the fruit seller bought it for 10% less. Then, we’ll determine the cost price that the seller initially paid for the mangoes. Here’s how we do it:
Let’s suppose the original cost price (before 10% discount) is Rs. x per kg.
Since the fruit seller sells mangoes at a 20% profit, it means he sells it for 120% of the cost price. Therefore, we have:
120/100 * x = Rs. 110
Solving for x, we find:
x = Rs. 110 * 100 / 120 = Rs. 91.67 approximately
Now, this is the cost price of the mangoes before the 10% discount. But we know the fruit seller bought it for 10% less. So, the price he paid (the cost price) would be:
90% of Rs. 91.67 = 90/100 * Rs. 91.67 = Rs. 82.5 approximately
So, the cost price for the fruit seller would be approximately Rs. 82.5 per kg.

(9) If 20% of a number is 30, what is 40% of that number?

• (a)60
• (b)70
• (c)80
• (d)65

Answer

Correct Answer : (a) 60
To find out what 40% of a number is, we first need to determine the value of the number itself based on the given information.
Let’s assume the number is “x.”
According to the given information, 20% of the number is 30:
0.20x = 30
To find the value of x, we can divide both sides of the equation by 0.20:
x = 30 / 0.20
x = 150
Therefore, the value of the number is 150.
Now, we can calculate 40% of that number:
40% of 150 = (0.40)(150) = 60
Hence, 40% of the number 150 is 60.

(10) In a class of 50 students, 30% of the students play football, 40% of the students play cricket. What percent of students play neither?

• (a)35 Percentage
• (b)27 Percentage
• (c)30 Percentage
• (d)33 Percentage

Answer

Correct Answer : (c) 30 Percentage
In a class of 50 students, 30% of the students play football and 40% of the students play cricket.
This means that 30% + 40% = 70% of the students play at least one of the two sports.
Therefore, 100% – 70% = 30% of the students play neither football nor cricket.