# Crack IBPS PO : Averages | Aptitude day 66

D.1-10) Study the following and answer the questions:

Q.1) The average age of the husband and the wife is 27 years when they got married 6 years ago. But now the average age of husband, wife & child was 24 years. How old is the child now?

a) 6 yrs

b) 7yrs

c) 8yrs

d) 9yrs

e) 5yrs

a)

The total age of husband & wife now = (27×2)+(6×2)= 66 yrs

Total age of husband, wife & child now = 24 × 3 = 72 yrs

Age of child = 72 – 66 = 6 yrs

Q.2) The average of height of the students in a class was 180cm. When 5 student’s whose average height is 146.4cm are newly admitted The average height of the class was reduced by 12cm. How many students are present in the class?

a) 9

b) 5

c) 13

d) 14

e) 10

d)

Let the number of students initially in the class be N

(1)àThen, total Height = N × 180 ——————-(1)

Again the no of students increased = N + 5

(2)àThen, total height N + 5 students = (N+5)× 168 ———-(2)

(3)àThe total height of 5 new students = 5 × 146.4 = 732cm. –(3)

From 1,2 & 3,

(N + 5)×168 – 732 = N × 180

168N +840 – 732 = 180N => N = 9

Therefore , number of students in class = 9 + 5 = 14

Q.3) Find the average of even numbers between 251 & 401?

a) 320

b) 322

c) 324

d) 326

e) 328

d)

No of even numbers below 401 = 200

No of even numbers below 251 = 125

No of even numbers between 251 & 401 = 75

Sum of first N even numbers = N(N+1)

Sum of even number between 251 & 401=[200(200+1) ]–[125(125+1) ]=24450

Average of even numbers between 251 & 401 = 24450/75 = 326

Q.4) Arun married 7 years ago at the age of 30 years. His wife’s present ageis 33years. If 8 years later from marriage the average age of Arun, his wife and their son was 30 years, then what is son’s present age?

a) 5yr

b) 4yrs

c) 3yrs

d) 2yrs

e) None of these

b)

Arun’s present age = 37 yrs

Total age of family after 8 yrs from marriage = 30 × 3 = 90

Present age Arun & his wife = 37+33 = 70 yrs

Present age of arun, his wife & his son = 90 – 8×3 = 66

Present age of son = 70-66 = 4yrs.

Q.5) The average score of a cricketer for 11 matches is 44 runs. If the average for the first 6 matches is 42, then find the average for the last 5 matches is,

a) 42.8 runs

b) 46.4 runs

c) 48.2 runs

d) 50 runs

e) None of these

b)

Total score of cricketer for 11 matches = 11×44 = 484 runs

Total score of cricketer for first 6 matches = 6 × 42 = 252 runs

the average for the last 5 matches = (484-252)/5=46.4

Q.6) The average scores of a group of students in a test is 142. The 23% of student’s average score is 126 and 51% of student’s average score is150. Then find the average score of remaining 26% of students approximately,

a) 134

b) 136

c) 140

d) 142

e) 144

C)

Let the number students be 100,

Then,

100×142 = 23×126 + 51×150 + 26×X

26X = 14200 – 2898 – 7650 => X = 140.4 = 140(Approx)

Q.7) In the first 15 over’s of a cricket game, the run rate was only 8. What should be the run rate in the remaining 35over’s to reach the target of 557.5 runs?

a) 12.5 runs per over

b) 14 runs per over

c) 10.6 runs per over

d) 13.5 runs per over

e) None of these

a)

Total runs scored in first 15 overs = 120

Remaining runs to be scored = 557.5 – 120 = 437.5 runs

Run rate in 35 overs = 437.5/35 = 12.5 runs

Q.8) The average weight of three boys A, B and C is 75 kg, while the average weight of three boys B, D and E is 102 kg. What is the average weight of A, B, C, D and E?

a) 78kg

b) 80 kg

c) 82kg

e) None of these

d)

Total weight of (A + B + C)= (75 × 3)= 225 kg.

Total weight of (B + D + E)= (102 × 3)kg = 306 kg

Adding both, we get: A + 2B + C + D + E = 225 + 306 kg = 531 kg

So, to find the average weight of A, B, C, D and E, we ought to know B’s weight, which is not given.

Q.9) The average age of A and B is 24 years. If C replaced A, the average would be 20 and if C replaced by B, the average would be 22. What are the ages of A, B and C respectively?

a) 18, 26, 22

b) 22, 16, 26

c) 26, 18, 22

d) 26, 22, 18

e) None of these

d)

Total age of A & (1)àB = 24 × 2 = 48 yrs —(1)

Total age of B & (2)àC = 20 × 2 = 40 yrs —(2)

Total age of A & (3)àC = 22 × 2 = 44 yrs —-(3)

From 1,2 & 3,

(4)àA + B+ C = 66 —————————(4)

From 1& 4, C= 18

From 2& 4, A= 26

From 3& 4, B= 22

Q.10) The average weight of 12 men is decreased by 6 kg when one of them weighing 250 kg is replaced by another person. This new person is again replaced by another person whose weight is 34 kg lower than the person he replaced What is the overall change in the average due to these dual changes?

a) 6kg

b) 12kg

c) 18kg

d) 20kg

e) None of these

C)

Let the average weight of 12 persons be X kg and the weights of the persons, entered the group for the

first time and second time be (P)and (P-34)kg respectively,

From the question,

(12X-250+P)/12 =X-6 => P=178

Another person (P-34)= 178 – 34 = 144

(12X-144)/12 =X-r => r=12

Therefore the overall change = 6 + 12 =18kg
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