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Average and Age Questions

41. Present ages of Mukti and Shakti are in the ratio 5: 6, respectively. Ages of Neeti and Kriti after three years will be in the ratio of 12: 7, respectively. Present average age of Mukti, Shakti and Kriti is 28 years. Find the present age of Shakti if the present average age of Mukti, Neeti and Kriti is 27 years.




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Correct Ans:36 years
Explanation:
Let the present ages of Mukti and Shakti be 5x years and 6x years, respectively
Let the ages of Neeti and Kriti three years hence be 12y years and 7y years, respectively
So, the present ages of Neeti and Kriti are (12y – 3) years and (7y – 3) years, respectively
According to the question:
5x + 6x + 7y - 3 = 28*3
11x + 7y = 87 --------- (1)
Also, 5x + 12y - 3 + 7y - 3 = 27*3
5x + 19y = 87 ---------- (2)
Solving both equ (1) and (2) we get,
-174y = -522
y = 3
Sub y = 3 in equ (1)
11x = 87 - 21 = 66
x = 6
So, the present age of Shakti = 6*6 = 36 years
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42. 8 years ago, the age of the father and son is in the ratio of 5 : 2. 7 years hence, the age of the father and his son is in the ratio of 13 : 7. The average Present age of the father, mother, son and daughter is 38. The difference between the age of the mother and her daughter is 34. Then find the present age of the daughter?




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Correct Ans:16 years
Explanation:
8 years ago, the ratio of age of the father and his son = 5 : 2 (5x, 2x)
7 years hence, the ratio of age of the father and his son = 13 : 7
According to the question,
(5x + 15)/(2x + 15) = (13/7)
35x + 105 = 26x + 195
9x = 90
x = 10
The present age of the father and his son = (5x + 8), (2x + 8) = 58, 28
The average Present age of the father, mother, son and daughter = 38
Total Present age of the father, mother, son and daughter = 38*4 = 152
Total present age of the mother and her daughter = 152 - 86 = 66
Let the present age of mother and daughter be A and B,
A + B = 66 --------- (1)
A - B = 34 --------- (2)
By solving equation (1) and (2),
2A = 100
A = 50
Sub A = 50 in equ (1)
B = 66 - 50 = 16
So, the present age of daughter = 16 years
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43. The average salary per head of all the workers of an office is Rs 75. The average salary of 25 officer is Rs 625 and the average salary of the rest is Rs 65. Find the total numbers of workers?




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Correct Ans:1400
Explanation:
Let total no. of workers = x

Total salary = x × 75 ..... (i)

again, as per the question

Total salary = 25 × 625 + (x – 25) × 65 ..... (ii)

From (i) & (ii)

x × 75 = 25 × 625 + (x – 25) × 65
75x – 65x = 15625 – 1625

10x =14000

x = 1400

Hence, Total numbers of workers is 1400.
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44. There are 14 people in a family and the average age of all the family members is 30 years. A new baby born in a family, After 4 years what will be the average age of the all family members?




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Correct Ans:32
Explanation:
The total age of all family members = 30 × 14 = 420

New baby born and after 4 years the total age of all the members = 420 + 15 × 4 = 420 + 60 = 480

Reqd average = 480 /15 = 32 years

Hence, 32 years is correct.
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45. The average of 19 numbers is 8. If the average of the first 9 numbers be 11 and the average of last 9 numbers be 9, then the middle number is?




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Correct Ans:28
Explanation:
As per the given information, we get

Average of 19 numbers = 8. So, total of the numbers = 19× 8 = 152

Average of first 9 numbers = 11. So, total of the numbers = 11 × 9 = 99

Average of last 9 numbers = 9. So, total of the numbers = 9 × 9 = 81

Hence, the 10th number = (99+81) – 152 = 180– 152 = 28.

Hence, the answer is 28.
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46. Ten years ago, sum of age of mother & son is 16 years less than present age of father and age of mother at the time of birth of son is 32 years less than father"™s present age. If after six-year ratio of age of son and mother will be 6 : 11, then find average of present age of mother and father?




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Correct Ans:45 years
Explanation:
Let present age of father, mother & son be 'f ', 'm' & 's' respectively
(m -10) + (s - 10) = f - 16
m + s = f + 4
f = m + s - 4 ------------ (i)
Mother's age when son is born = m - s
Given, m - s = f - 32
f = m - s + 32 ---------- (ii)
From (i) and (ii)
m + s - 4 = m - s + 32
2s = 36
s = 18 years
Given, (s + 6)/(m + 6) = 6/11
11s + 66 = 6m + 36
6m + 36 = 264
6m = 228
m = 38 years
From (i) we get,
f = 52 years
Required average = (38 + 52)/2 = 45 years
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47. Average weight of three friends X, Y and W is 50 kg. Another person Z joins the group and now the average is 66 kg. If another person U whose weight is 6 kg more than Z, joins the group replacing X, then average weight of Y, W, Z and U becomes 75 kg. What is the weight of X (in kg)?




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Correct Ans:84 kg
Explanation:
Total weight = Average weight * No of persons

Total weight of X, Y and W = 50 × 3 = 150 kg

Again, X + Y + W + Z = 66 × 4 = 264 kg ......... (i)

Weight of Z = 264 – 150= 114 kg

Weight of U = 114 + 6 = 120 kg

Now, as per the question

Y + W + Z + U = 75 × 4 = 300 kg. ................... (ii)

Subtracting (i) from (ii), we get

U – X = 120 – X = 300 – 264 = 36

Therefore, weight of X = 120 – 36 = 84 kg

Hence, The weight of X is 84 kg
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48. In an exam of 200 marks, the average marks of a class of 50 students are 86. If the top 3 scorers of the class leave, the average score falls “down by 1. If the other two toppers except “the highest topper scored not more than 95. “then what is the minimum score the topper can score?          




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Correct Ans:115
Explanation:
Total score = no of student * average mark
Total score of 50 students = (50 × 86) =4300

Total score of top 3 scorers = Total score of 50 students – score of without topper’s
Total score of top 3 scorers = 4300 – (47 × 85) = 305

To minimize the score of the top scorer,(from question)
we assume the other two top scorers score the maximum they can = 95 marks each.

Two top scorers score = (95+95) = 190

The top scorer scored = Total score of top 3 scorers - two top scorers score
So, the top scorer scored = 305 – 190 = 115 marks.

Hence, The the topper’s minimum score is 115 marks.
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49. The average annual income (in Rs.) of certain agricultural workers is S and that of other workers is T. The number of agriculture workers is 11 times that of other workers. Then the average monthly income (in Rs.) of all the workers is?




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Correct Ans:(11S + T)/12
Explanation:
Let the number of other workers be Z.
Then, number of agricultural workers = 11Z
Total number of workers = 12Z
So, Average monthly salary = (S * 11Z + T * Z)/12Z
= (S * 11 + T)Z / 12Z = (11S + T)/12
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50. Ratio of ages of A to B, 4 year before from now was 8 : 5 and ratio of ages of B to C, 3 years hence will be 9 : 11. If the present average age of B and C is 27 years then find the present age of A.




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Correct Ans:36 years
Explanation:
Let ages of 8 and C is 3 years hence is 9x and 11x respectively.
So, (9x- 3) + (11x- 3) = 27 * 2
20x - 6 = 54
20x = 60
x = 3
So present age of B = (9*3 - 3) = 24 years
Let present age of A = y years
(y - 4)/(24 - 4) = 8/5
5y - 20 = 160
5y = 180
y = 36 years.
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51. Piya got married 5 years ago, today her age is 1(1/3) time her age at the time of marriage. What is present age of Piya (in years)?




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Correct Ans:20
Explanation:
Let present age be x
Let the age of Piya when she got married = x - 5
x = (x - 5) * (4/3)
3x = 4x - 20
4x - 3x = 20
x = 20
The present age of Piya is 20 years.
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52. The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. The mean salary of remaining workers is:




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Correct Ans:Rs. 6000
Explanation:
Given, Mean monthly salary of 75 workers = Rs.5680
---> Total monthly salary of 75 workers = 5680 * 75 = Rs. 4,26,000

Given, Mean salary of 25 of them = Rs.5400
---> Total monthly salary of 25 workers = 5400 * 25 = Rs. 1,35,000‬

Given, Mean salary of 30 others = Rs.5700
---> Total monthly salary of 30 other workers = 5700 * 30 = Rs. 1,71,000‬

Now, Total salary of the remaining workers (i.e., 20 other workers) = Total monthly salary of 75 workers - (Total monthly salary of 25 workers + Total monthly salary of 30 other workers)
= 4,26,000 - (1,35,000‬ + 1,71,000‬)
= 4,26,000 - 3,06,000‬
= 1,20,000‬

Average salary of the remaining workers (i.e., 20 other workers) = 1,20,000‬/20
= Rs. 6000
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53. Average age of A, B and C is 84 years. When D joins them the average age becomes 80 years. A new person, E, whose age is 4 years more than D, replaces A and the average of B, C, D and E becomes 78 years. What is the age of A?




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Correct Ans:80 years
Explanation:
Given, Average age of A, B and C = 84 years
----> Total age of A, B and C = 84 * 3
----> A + B + C = 252 ----> eqn (1)

When D joins them,
Average age = 80
---> Total age of A, B, C, and D = 80 * 4
---> A + B + C + D = 320 ----> eqn (2)

Now subtracting eqn (1) from eqn (2), we get
D's age = 320 - 252 = 68 years

Given, E's age = 4 + D's age = 4 + 68 = 72 years
Now, average age of B, C, D and E = 78 years
---> Total age of B, C, D and E = 78 * 4
---> B + C + D + E = 312
On substituting D's age and E's age in the above equation, we get
---> B + C + 68 + 72 = 312
----> (B + C)'s age = 172 years
On substituting this in equation (1), we get
A + 172 = 252
---> A = 252 - 172
----> A's age = 80 years
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54. Ratio of present age of X & Y is 5 : 4. At the time X & Y got married this ratio was 6 : 4. After 4 years this ratio became 9 : 8. How many years ago did X & Y got married?




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Correct Ans:2
Explanation:
Let the present age of X and Y be 5a, 4a
If they got married t years ago,
(5a - t)/(4a - t) = 6/4
(5a - t)/(4a - t) = 3/2 ----------------eqn (1)
After 4 years from now, their age ratio becomes
(5a + 4)/(4a + 4) = 9/8 ---------------- eqn (2)
Now from equation 1 and 2, equation 2 can be solved easily.
Taking equation 2 to find a,
(5a + 4)/(4a + 4) = 9/8
8(5a + 4) = 9(4a + 4)
40a + 32 = 36a + 36
4a = 4
a = 1.
Now substitute the value of a in equation 1, we get
(5(1) - t)/(4(1) - t) = 3/2
(5 - t)/(4 - t) = 3/2
2(5 - t) = 3(4 - t)
10 - 2t = 12 - 3t
t = 2 years.
Hence, X & Y got married 2 years ago.
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55. Average age of A,B and C is 74 years. When D joins them the average age becomes 68 years. A new person, E, whose age is 4 years more than D, replaces A and the average of B,C, D and E becomes 64 years. What is the age of A?




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Correct Ans:70 years
Explanation:
We know that Average = sum of elements/number of elements
Given :
Average age of A, B, C = (A + B + C)/3 = 74
A + B + C = 3*74 = 222 years ----> eqn (1)

Average of A, B, C, D = (A + B + C + D)/4 = 68
A + B + C + D = 4*68 = 272 years ----> eqn (2)

Now subtracting eqn (1) from eqn (2), we get
D's age = 272 - 222 = 50 years.

Given, E's age = 4 + D's age
= 50 + 4 = 54 years.
So A is replaced by E
Average age of B, C, D, E = (B + C + D + E)/4 = 64
B + C + D + E = 64*4 = 256 years.
On substituting D's age and E's age in the above equation, we get
---> B + C + 50 + 54 = 256
----> B + C = 152
On substituting this in equation (1), we get
A's age = 222 - 152 = 70 years. (from 1)
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56. The ages of Rita, Seema, Arun and Ramesh are in arithmetic progression, but not in order. The ratio of ages of Rita and Seema is 6 : 4 and Arun to Ramesh is 8 : 10. Two years later the age of Seema and Ramesh will be 2 : 3. Find the ratio of ages of Rita and Arun 




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Correct Ans:3 : 4
Explanation:
We know that arithmetic progression (A.P) form is a, a + d, a + 2d...
Given:
Here the ratio of Seema to Rita = 4 : 6
= 2 : 3 = 2x : 3x
And ratio of Arun to Ramesh = 8 : 10
= 4 : 5 = 4y : 5y
But their ages are in A.P. So, the difference between two consecutive terms is always the same.
So 3x - 2x = 5y - 4y
On equating we get
x = y.
Therefore the ages of Seema, Rita, Arun, Ramesh is given by 2x, 3x, 4x, 5x
After 2 years ratio of Seema to Ramesh =
(2x + 2) / (5x + 2) = (2/3)
3(2x + 2) = 2(5x + 2)
(6x + 6) = (10x + 4)
4x = 2
x = 1/2
Age of Seema = 2*(1/2) = 1yr
Age of Rita = 3*(1/2) = 3/2 yr
Age of Arun = 4*(1/2) = 2 yr
Age of Ramesh = 5*(1/2) = 5/2 yr
So the ratio of ages of Rita and Arun = (3/2) /2
= 3/4 or 3 : 4
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57. The batting average for 50 innings of a cricket player is 60 runs . His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 48 innings is 58 runs. The highest score of the player is




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Correct Ans:194
Explanation:
Given:
Highest score - Lowest score = 172 runs.-----(1)
Total runs scored by player in 50 innings = 50*60
= 3000 runs.
Total runs scored by the player in 48 innings (after excluding two innings) = 48*58
= 2784 runs.
Sum of the scores of the excluded innings = 3000 - 2784
= 216 runs.

So,
Highest score + Lowest score = 216 runs.------(2)

Now adding eqn (1) and (2), we get

Highest score - Lowest score = 172 runs.
Highest score + Lowest score = 216 runs. -- (Here Lowest scores cancels each other on adding)
---> Highest score = (388/2) = 194.
Hence the highest score = 194 runs.
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58. Average score of Robin, Mani and Sabi is 63. Robin's score is 15 less than Arun and 10 more than Mani. If Arun scored 30 marks more than the average scores of Robin, Mani and Sabi, what is the sum of Mani's and Sabi's scores?




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Correct Ans:111
Explanation:
Given that,
(Robin + Mani + Sabi)/3 = 63
Robin's score = Arun - 15
And, Robin's score = Mani + 10
Arun's score = (Robin + Mani + Sabi)/3 + 30
= 63 + 30 = 93
Robin's score = 93 - 15 = 78
The sum of Mani's and Sabi's score,
(Robin + Mani + Sabi)/3 = 63
78 + Mani + Sabi = 189
Mani + Sabi = 189 - 78 = 111
Therefore, the sum of Mani's and Sabi's score = 111
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59. Present age of Anu is 12.5% more than that of Asha and present age of Deena is 12.5% less than that of Asha. Ratio of present age of Dharsh & Siva is 4 : 3 and present age of Deena is equal to age of Dharsh four years hence. If average age of Dharsh & Siva after three years will be 24 years, then find average age of Anu & Siva after six years?




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Correct Ans:33 years
Explanation:
Ratio of Anu, Asha and Deena = 112.5 : 100 : 87.5 = 1125 : 1000 : 875
Anu : Asha : Deena = 9 : 8 : 7
Present age of Dharsh and Siva be 4x & 3x respectively.
Average age of Dharsh & Siva after three years = 24 years
(4x + 3 + 3x + 3)/2 = 24
7x + 6 = 48
7x = 42
x = 6
Present age of Dharsh = 24 years
Present age of Siva = 18 years
Present age of Deena = Dharsh + 4 = 28 years
Present age of Anu = 28*(9/7) = 36 years
Required average age = (36 + 18 + 6 + 6)/2 = 33 years
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60. A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?




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Correct Ans:Rs. 7.98
Explanation:
Total quantity of petrol consumed in 3 years = (4000/7.50 + 4000/8 + 4000/8.50) liters
= 4000 (100/750 + 1/8 + 100/850)
= 4000 (2/15 + 1/8 + 2/17)
= 4000 [(272 + 255 + 240)/2040]
= 4000 [767/2040]
= 76700/51 liters

Total amount spent in 3 years = Rs. 4000 * 3 = Rs. 12000.

Average cost per litre of petrol for 3 years = Total amount spent in 3 years / Total quantity of petrol consumed in 3 years
= Rs. (12000*51/76700)
= 120*51 / 767
= 6120/767
= Rs. 7.98
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