Aptitude : Problems on Average

(21) The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result.

• (a)55
• (b)56
• (c)57
• (d)58

Answer

Correct Answer : (b) 56
Let’s denote the results as X1, X2, …, X11.
The average of all 11 results is 50, so the sum of all results is 50*11 = 550.
The average of the first six results is 49, so the sum of the first six results is 49*6 = 294.
The average of the last six results is 52, so the sum of the last six results is 52*6 = 312.
Note that the sixth result is included in both groups, so when we sum up the first six results and the last six results, we are adding the sixth result twice.
Therefore, 550 (sum of all results) = 294 (sum of first six) + 312 (sum of last six) – X6 (the sixth result).
So, X6 = 294 + 312 – 550 = 56.

(22) A student’s average marks were 63 per paper. After re-evaluation, his average marks got increased to 65 per paper. Due to re-evaluation he got 50 extra marks. How many papers were there in total?

• (a)25 papers
• (b)30 papers
• (c)35 papers
• (d)15 papers

Answer

Correct Answer : (a) 25 papers
Let’s denote the total number of papers as ‘n’.
Before re-evaluation, the student’s average marks were 63 per paper. Therefore, the total marks obtained initially were 63n.
After re-evaluation, his average marks increased to 65 per paper. Therefore, the total marks obtained after re-evaluation were 65n.
The increase in marks due to re-evaluation was 50. So we can write the equation as:
65n – 63n = 50,
2n = 50,
n = 50 / 2,
n = 25.
So, there were 25 papers in total.

(23) The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?

• (a)50 kg
• (b)85 kg
• (c)35 kg
• (d)45 kg

Answer

Correct Answer : (b) 85 kg
The weight of the new person is 85 kg.
The total weight of the 8 people before the new person came in is 8 * 65 = 520 kg.
The total weight of the 8 people after the new person came in is 8 * (65 + 2.5) = 550 kg.
The weight of the new person is 550 – 520 = 30 kg.
Therefore, the weight of the new person is 85 kg.

(24) The average age of A, B, C is 45 years. If the average age of A and B be 40 years and that of B and C be 43 years, then find the age of B.

• (a)31 years
• (b)30 years
• (c)32 years
• (d)33 years

Answer

Correct Answer : (a) 31 years
Let’s denote the ages of A, B, and C as ‘a’, ‘b’, and ‘c’ respectively.
Given that the average age of A, B, C is 45 years, the total of their ages is 3 * 45 = 135 years. So, we have:
a + b + c = 135. (Equation 1)
The average age of A and B is 40 years, so the sum of their ages is 2 * 40 = 80 years. Therefore:
a + b = 80. (Equation 2)
Similarly, the average age of B and C is 43 years, so the sum of their ages is 2 * 43 = 86 years. Therefore:
b + c = 86. (Equation 3)
Subtracting Equation 2 from Equation 1 gives:
c = 135 – 80 = 55.
Substituting c = 55 into Equation 3 gives:
b + 55 = 86,
b = 86 – 55,
b = 31.
So, the age of B is 31 years.

(25) The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. Find the monthly income of A, B and C.

• (a)5,00,06,10,06,400 rupes respectively
• (b)4,00,06,10,06,400 rupes respectively
• (c)40,00,50,06,400 rupes respectively
• (d)4,00,06,20,06,400 rupes respectively

Answer

Correct Answer : (b) 4,00,06,10,06,400 rupes respectively
Let’s denote the monthly incomes of A, B, and C as ‘a’, ‘b’, and ‘c’ respectively.
Given that the average monthly income of A and B is Rs. 5050, the sum of their incomes is 2 * 5050 = Rs. 10100. So, we have:
a + b = Rs. 10100. (Equation 1)
The average monthly income of B and C is Rs. 6250, so the sum of their incomes is 2 * 6250 = Rs. 12500. Therefore:
b + c = Rs. 12500. (Equation 2)
Similarly, the average monthly income of A and C is Rs. 5200, so the sum of their incomes is 2 * 5200 = Rs. 10400. Therefore:
a + c = Rs. 10400. (Equation 3)
Subtracting Equation 2 from the sum of Equation 1 and Equation 3 gives:
(a + b) + (a + c) – (b + c) = Rs. 10100 + Rs. 10400 – Rs. 12500,
2a = Rs. 8000.
Solving for a, we get:
a = Rs. 8000 / 2 = Rs. 4000.
Substituting a = Rs. 4000 into Equation 1 and Equation 3 gives:
b = Rs. 10100 – Rs. 4000 = Rs. 6100,
c = Rs. 10400 – Rs. 4000 = Rs. 6400.
So, the monthly incomes of A, B, and C are Rs. 4000, Rs. 6100, and Rs. 6400 respectively.