Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

\text{The average age of 25 students of a class is 13 years. If the age of teacher is also included, the average age is increased by 2 years. Find the age of teacher.}

  1. 64 years

  2. 65 years

  3. 63 years

  4. 70 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 25 students = 25 × 13 = 325 years. With teacher included (26 people), average = 15 years, so total = 26 × 15 = 390 years. Teacher's age = 390 - 325 = 65 years. Options A (64), C (63), and D (70) are incorrect.

Multiple choice

The average score of a class of boys and girls in an examination is N. The ratio of boys and girls in the class is 4:1 .If the average score of the boys is (N+1),then the average score of the girls is-
  1. $\(N-1\)$
  2. $\(N-2\)$
  3. $\(N-4\)$
  4. $\(2N+1\)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With boys:girls = 4:1, let 4x boys and x girls total. Class average N gives total score 5xN. Boys contribute 4x(N+1). Girls contribute 5xN - 4xN - 4x = xN - 4x, so girls' average = (xN - 4x)/x = N - 4.

Multiple choice

Average marks of a student in 5 different subjects is 65, if he gets 23 marks in English, 35 marks in Sanskrit, 178 marks in math’s and 49 marks in Hindi then find the marks received by the student in history? 5 विषयों में एक छात्र के औसत अंक 65 हैं। यदि वह अंग्रेज़ी में 23 अंक, संस्कृत में 35 अंक, गणित में 178 अंक और हिंदी में 49 अंक प्राप्त करता है तो इतिहास में कितने अंक प्राप्त करेगा?

  1. 45

  2. 40

  3. 49

  4. 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marks for 5 subjects = 65 × 5 = 325. Sum of marks in 4 subjects = 23 + 35 + 178 + 49 = 285. Therefore, marks in History = 325 - 285 = 40.

Multiple choice

The average of a students in the first 50 test is p and his average of the next 10 series is q. If his overall average is ( p +2 ). then what is q in terms of p ? एक छात्र के प्रथम 50 टेस्ट मैचो का औसत p है और अगली 10 सीरीज का औसत q है . यदि कुल औसत ( p +2 ) है तो q को p के रूप में क्या लिख सकते है ?

  1. p + 6

  2. p + 8

  3. p + 10

  4. p + 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks from first 50 tests = 50p. Total marks from next 10 tests = 10q. Overall average for 60 tests is (p+2), so total = 60(p+2) = 60p + 120. Equating: 50p + 10q = 60p + 120, which gives 10q = 10p + 120, so q = p + 12.

Multiple choice

The average weight of 24 boys was recorded as 62 kgs. If the weight of the teacher was added, the average increased by 1 kg. What was the teacher's weight?

  1. 88 kg.

  2. 92 kg.

  3. 87 kg.

  4. 77 kg.

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight of 24 boys = 24 × 62 = 1488 kg. With teacher, 25 people average 63 kg, so total = 25 × 63 = 1575 kg. Teacher's weight = 1575 - 1488 = 87 kg. When adding a value to a set, it changes the average by (new value - old average)/(n+1).

Multiple choice

A group of four persons consist of two men A and B, and two women C and D. The average weight of all four is 55 kg. The average weight of the two men is over 60 kg. D weight more than 52 kg. In this content which one of the following statements follows logically? चार व्यक्तियों के एक समूह में A और B दो पुरूष, तथा C और D दो स्त्रियां है। चारों का कुल औसत वजन 55 किग्रा. है। दोनों पुरूषों का औसत वजन 60 किग्रा. से अधिक है। D का वजन 52 किग्रा. से अधिक है इसके बारे में निम्नलिखत में से कौन सा एक कथन युक्ति संगत है?

  1. Any man weights more than any women /कोई भी पुरूष किसी भी स्त्री से अधिक वजन वाला है।

  2. C's weights less than 49 kg/C का वजन 49 किग्रा. से कम है।

  3. C's weight is the lowest/C का वजन सबसे कम है।

  4. Either of the men weight more than 60 kg./किसी भी पुरूष का वजन 60 किग्रा. से अधिक है।
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of 4 persons = 4×55 = 220 kg. Men's average > 60, so men's total > 120 kg. Therefore women's total = 220 - (men's total) < 220 - 120 = 100 kg. So women's average < 100/2 = 50 kg. Since D > 52 kg and C + D < 100 kg, we have C < 100 - 52 = 48 kg. So C < 48 kg, which means C's weight is definitely less than 49 kg.

Multiple choice

The average weight of 60 children of a class is 38.5 kg ,when five more children with weights 41.6 kg ,36.8 kg, 38.8 , 42.2 kg and 36.6 kg join the class the average weight of the 65 children in the class is- एक कक्षा के 60 बच्चों का औसत भार 38.5 किग्रा है, तब उस कक्षा में 41.6 किग्रा. 36.8किग्रा. 38.8 किग्रा. 42.2 किग्रा.और 36.6 किग्रा. के पांच बच्चे और आ गये तो कक्षा के 65 बच्चों का औसत भार है-

  1. 38.5 kg/ किग्रा

  2. 36.6 kg/ किग्रा

  3. 39.4 kg/ किग्रा

  4. 41.2 kg/ किग्रा
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight of 60 children = 60 × 38.5 = 2310 kg. Weight of 5 new children = 41.6 + 36.8 + 38.8 + 42.2 + 36.6 = 196 kg. New total = 2506 kg. New average = 2506 ÷ 65 ≈ 38.55 kg, which rounds to 38.5 kg. Option A is correct.

Multiple choice

The average weight of 21 boys is 68 kgs. If the teacher's weight is included, the average weight is increased by 1 kg. What is the teacher's weight?
  1. $86 kgs.$
  2. $64 kgs.$
  3. $72 kgs.$
  4. $92 kgs.$
  5. $90 kgs.$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total weight of 21 boys = 21 × 68 = 1428 kg. When teacher is included, total people = 22, new average = 69 kg. New total weight = 22 × 69 = 1518 kg. Teacher's weight = 1518 - 1428 = 90 kg. Alternatively, use the shortcut: teacher's weight = new average + (number of boys × increase) = 69 + 21 = 90 kg.

Multiple choice

In a class, the average age of boys is 14 years and that of girls is 12 years. The number of girls is 8 more than the number of boys . What is the average age of all students in the class ? एक कक्षा के लड़कों की औसत आयु 14 वर्ष है, और लड़कियों की औसत आयु 12 वर्ष है। लड़कियों की संख्या लड़को की संख्या से 8 अधिक है। कक्षा में सभी विद्यार्थियों की औसत आयु क्या है?

  1. 12.5

  2. 13.5

  3. 14.5

  4. Data inadequate /आंकड़े अधूरे है
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let number of boys = b. Then number of girls = b + 8. Total average = (14b + 12(b+8)) / (2b + 8) = (26b + 96) / (2b + 8). This expression depends on b - different values of b give different averages. Without knowing b or total students, we cannot determine a unique numerical answer. For example: if b=8, average = 13.6; if b=12, average ≈ 13.33.

Multiple choice

There are 100 students in 3 sections A, B and C of a class. The average marks of all the 3 sections was 84. The average of B and C was 87.5 and the average marks of A is 70. The number of students in A was ? एक कक्षा के तीन सेक्शनों A, B और C में 100 छात्र हैं। तीनों सेक्शनों के औसत अंक 84 हैं। B और C का औसत 87.5 और A के औसत अंक 70 थे। । A में छात्रों की संख्या कितनी थी?

  1. 15

  2. 25

  3. 30

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let students in A = a, B = b, C = c. Total: a + b + c = 100. Overall avg 84, so total marks = 8400. Avg of A = 70, so marks in A = 70a. Avg of B and C = 87.5, so marks in B + C = 87.5(b + c). Also 70a + 87.5(b + c) = 8400. Substituting b + c = 100 - a: 70a + 87.5(100 - a) = 8400. Solving: -17.5a + 8750 = 8400, giving a = 20.

Multiple choice

The average age of a five member family is 20, if one member goes then average is equal to 15. what is the age of member which was gone? एक परिवार के पांच सदस्यों का औसत 20 है। यदि एक सदस्य चला जाता है तब परिवार का औसत 15 के बराबर हो जाता है । उस सदस्य की उम्र क्या होगी जो चला गया था?

  1. 20

  2. 30

  3. 40

  4. 50
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 5 members with average age 20, total age = 5 x 20 = 100 years. When one member leaves, 4 members remain with average 15, so their total age = 4 x 15 = 60 years. The age of the member who left = 100 - 60 = 40 years. This follows directly from the definition of average.