Solution :-
Detailed exaplanations
1.(5) According to the question,
Sum of five numbers = 5 × 3.6.4
= 1532
∴ Third number
= 1532 – 2 × 431 – 2 × 214.5
= 1532 – 862 – 429 = 241
2.(4) Required average
= (1050 + 1020)/(65 + 50)
= 2070/115 = Rs. 18
3.(5) Third number
= 290 – 2 × 48.5 – 2 × 53.5
= 290 – 97 – 107 = 86
4.(4) Actual weight of 53 girls
= 53 × 58 + 45 – 65
= 3074 + 45 – 65 = 3054 kg
∴ Required actual average weight
= 3054/53 = 57.62 kg.
Or
Decrease in weight = 65 – 45
= 20 kg
∴ Required actual average weight
= 3054/53 = 57.62 kg
Or
Decrease in weight = 65 – 45 = 20 kg
∴ Required actual average weight
= (58 – 20/53) kg = 57.62
5.(2) Difference of marks
= 72 + 61 – 48 – 65 = 20
∴ Correct average marks
= 68 + 20/20 = 69
6.(2) Total age of 5 member family = 24 × 5 = 120 years
Total age 8 years ago
= 120 – 5 × 8 = 80 years
∴ Required average age
= 80/5 = 16 years
7.(2) The third number .
= 5 × 65 – 2 × 81 – 2 × 38
= 325 – 162 – 76 = 87
8.(1) According to question.
P + C + M = 120 + C
P + M = 120
Average = 120/2 = 60
9.(1) (Tricky Approach)
Let the required average be x years
then 80 × 15 = 15 × 16 + 25 × 14 + 40 × x
= 40x = 1200 – 240 – 350 = 610
∴ x = 610/40 = 15.25 years
10.(2) Age of the fourth boy
= (26 × 7 – 3 × 19 – 3 × 32) years
= (182 – 57 – 96) years
= 29 years
