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- Question
After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
Options- A. 12
- B. 13
- C. 14
- D. 15
- Correct Answer
- 15
Explanationi) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years.
- 1. The mean temperature of Monday to Wednesday was 37 degree celsius and of Tuesday to Thursday was 34 degree celsius . If the temperature on Thursday was (4/5) th that of Monday, the temperature on Thursday was?
Options- A. 38 degree celsius
- B. 36 degree celsius
- C. 40 degree celsius
- D. 39 degree celsius Discuss
- 2. The average of 7 consecutive numbers is 20. The largest of these numbers is :
Options- A. 21
- B. 22
- C. 23
- D. 24 Discuss
- 3. The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :
Options- A. 45 kg
- B. 46 kg
- C. 47 kg
- D. 48 kg Discuss
- 4. The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
Options- A. 4
- B. 8
- C. 12
- D. 16 Discuss
- 5. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
Options- A. 70 kg
- B. 75 kg
- C. 80 kg
- D. 85 kg Discuss
- 6. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
Options- A. 45
- B. 40
- C. 39
- D. 37 Discuss
- 7. The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is :
Options- A. 35
- B. 36.5
- C. 40
- D. 42 Discuss
- 8. Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :
Options- A. 17
- B. 29
- C. 36
- D. 48 Discuss
- 9. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is :
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :
Options- A. Rs. 292.50
- B. Rs. 297.50
- C. Rs. 298
- D. Rs. 298.50 Discuss
Average problems
Search Results
Correct Answer: 36 degree celsius
Explanation:
Let, temperature of Monday = a Temperature of Tuesday = b Temperature of Wednesday = c Temperature of Thursday = 4a/5 Sum of temperatures of Monday to Wednesday = 3×37 = 111 => a+b+c=111------(1) Sum of temperatures of Tuesday to Thursday = 3×34 = 102 b+c+(4a/5) = 102 ------(2) (1)-(2)=> a−(4a/5)=111−102 a/5=9 a=45 Temperature on Thursday = 4a/5 =4×45/5 =36
Correct Answer: 23
Explanation:
Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23.
Correct Answer: 45 kg
Explanation:
Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.
Correct Answer: 8
Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
Correct Answer: 85 kg
Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Correct Answer: 40
Explanation:
Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2.
x/2 = (83 - 63) => x/2 = 20 => x = 40.
Correct Answer: 36.5
Explanation:
Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Correct Answer: 48
Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48.
Correct Answer: 3
Explanation:
Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be x years.
Then, age of the elder child = (x+2) years.
So, x+(x+2) =8 <=> x=3
Age of younger child = 3 years.
Correct Answer: Rs. 292.50
Explanation:
Let the average expenditure be Rs. x Then,
9x=[(8*30)+(x+20)]<=>9x =x+260 <=> x =32.50
Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50
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