Aptitude : Percentage

(1) A basketball player scored 150 points which included 5 three-pointers and 10 two-pointers. What percent of his total score did he make by free throws?

• (a)85.25 Percentage
• (b)87.45 Percentage
• (c)77.55 Percentage
• (d)76.67 Percentage

Answer

Correct Answer : (d) 76.67 Percentage
The total points from three-pointers = 5 * 3 = 15 points.
The total points from two-pointers = 10 * 2 = 20 points.
The total points from free throws = Total points – points from three-pointers – points from two-pointers
= 150 – 15 – 20 = 115 points.
The percent of his total score he made by free throws = (115 / 150) * 100 = 76.67%.

(2) In an exam, three students participated. One of them scored 15 marks more than the other and his marks were 60% of the sum of their marks. What were the marks obtained by each of them?

• (a)A = 30, B = 45, and C = 85
• (b)A = 30, B = 35, and C = 45
• (c)A = 30, B = 45, and C = 45
• (d)A = 30, B = 45, and C = 35

Answer

Correct Answer : (c) A = 30, B = 45, and C = 45
Let’s assume the marks of the three students are A, B, and C. According to the problem:
B = A + 15, and
C = 0.60 * (A + B).
Substituting B in the second equation we get:
C = 0.60 * (A + A + 15) = 0.60 * (2A + 15).
Therefore, the total marks are A + B + C = A + A + 15 + 0.60 * (2A + 15).
Solving this we get A = 30, B = 45, and C = 45.

(3) If P = x% of y and Q = y% of x, which of the following is true?

• (a)P != Q
• (b)P = Q
• (c)P > Q
• (d)P < Q

Answer

Correct Answer : (b) P = Q
P = x% of y = x/100 * y, and Q = y% of x = y/100 * x.
So, P = Q.

(4) In a school, 25% of students are below 10 years of age. The number of students above 10 years of age is 3/4 of the number of students of 10 years of age which is 60. What is the total number of students in the school?

• (a)120
• (b)130
• (c)150
• (d)140

Answer

Correct Answer : (d) 140
The number of students above 10 years of age = 3/4 * 60 = 45.
The total number of students over 10 and of 10 years = 45 + 60 = 105.
If 25% of students are below 10 years, then 75% of the students are 105.
Hence, the total number of students = 105 / 0.75 = 140.

(5) A student divided a number by 2/3 instead of 3/2. What is the percentage error in the calculation?

• (a)83.33 Percentage
• (b)70.5 Percentage
• (c)75.15 Percentage
• (d)80.45 Percentage

Answer

Correct Answer : (a) 83.33 Percentage
Let the number be x. The correct answer should be x * 3/2. However, the student mistakenly got it as x * 2/3. The error is therefore (x * 3/2) – (x * 2/3) = 5x/6. The percentage error is therefore (5x/6) / (x * 3/2) * 100% = 83.33%.

In other words, the student’s answer is 83.33% too low.