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Average
11. Six persons went to a hotel for meals. Five spent ₹32 each while the sixth spent ₹80 more than the average expenditure of all six. What was the total money spent?
32×5 + (x + 80) = 6x
160 + x + 80 = 6x
240 = 5x ⇒ x = 48
Total money spent = 6 × 48 = ₹288
12. The average age of a man and his son is 40 years. Their ages are in the ratio 11:5. Find the son’s age.
(11x + 5x)/2 = 40
16x/2 = 40 ⇒ 8x = 40 ⇒ x = 5
Son’s age = 5x = 25 years
13. Of three numbers, the second is twice the first and thrice the third. If their average is 44, find the largest number.
Second = 3x, First = 3x/2
x + 3x + 3x/2 = 132
11x/2 = 132 ⇒ x = 24
Largest number = 3x = 72
14. The average of five numbers is 58. The average of first two is 48.5 and last two is 53.5. Find the third number.
Sum of first two = 48.5 × 2 = 97
Sum of last two = 53.5 × 2 = 107
Third number = 290 − (97 + 107) = 86
15. The average of 13 papers is 40. The average of first 7 is 42 and last 7 is 35. Find marks of the 7th paper.
= 294 + 245 − 520
= 19
16. The average age of A and B is 20 years. If A is replaced by C, average becomes 19. If B is replaced by C, average becomes 21. Find ages of A, B and C.
B+C = 38
A+C = 42
Adding: 2(A+B+C)=120 ⇒ A+B+C=60
C=20, A=22, B=18
17. In a class of 50 students, average weight is 45 kg. When one leaves, average reduces by 100 g. Find weight of that student.
New total = 44.9×49 = 2200.1 kg
Required weight = 2250 − 2200.1 = 49.9 kg
18. The average age of 39 students is 15 years. Including teacher increases average by 3 months. Find teacher’s age.
New average = 15 years 3 months = 15.25 years
Total age (40 persons) = 610
Teacher’s age = 610 − 585 = 25 years
19. The average of 11 players increases by 2 months when two players aged 18 and 20 are replaced. Find average age of new players.
= 1 year 10 months
New players’ sum = 18 + 20 + 1 year 10 months
= 39 years 10 months
Average = 19 years 11 months
20. The average age of a class was 15 years. When 5 boys (average 12 years 6 months) joined, the average reduced by 6 months. Find original number of students.
15x + 12.5×5 = 14.5(x+5)
Solving gives x = 20
