The average of class in 35 yr. 6 new students with an average age of 33 yr. joined in that class, there by decreasing the average by half year. The original strength of the class was

Sum of 14 girls and teacher age = 15 x 15 = 225
Without teacher's age sum of 14 girls age = 14 x 14 = 196
? Teacher's age = 225 -196 = 29 year

Here, n = 21, a = 64, b = 65
Weight of teacher = n(b - a) + b
= 21( 65 - 64) + 65
= 21 + 65
= 86 kg

Here n= 34, a = 42 and b = 42.4
Weight of the teacher.
= n(b -a) + b
= 34 ( 42.4 - 42) + 42.4
= 13.6 + 42.4 = 56.0 kg

Here, n = 10, a = 60, b = 62
Number of runs scored in 11th inning
= n (b - a) + b
= 10 (62 - 60) + 62
= 20 + 62 = 82

Here n₁ = 19, a₁ = 74, n₂ = 38, a₁ = 63
Total average weight = (n₁a₁ + n₂ a₂) / (n₁ + n₂)
= [(19) (74) + (38) (63)] / (19 + 38)
= 3800/57 ? 67 kg

Total age of 5 members = 25 x 5 = 125 yr
Total age of 5 member and the servant
= (25 + 25 x 40/100) x 6
= 35 x 6 = 210 yr
? Age of the servant = 210 - 125 = 85 yr

Here, average decreases by 3 months of 3/12 yr.
Sum of ages decreased
= 30 x 3/12 = 15/2 = 7.5 yr
? Age of priyanka = (25 - 7.5) = 17.5 yr.

Temperature of (Mon + Tue + Wed) = 37 x 3 = 11°C

Temperature of (Tue + Wed + Thu) = 34 x 3 = 102°C

Temperature of (Mon - Thu) = 111°C - 102°C = 9°C

Temperature of [Mon - 4/5(Mon] = 9
Temperature of Monday = 9 x 5 = 45°C

? Temperature of Thursday = 45 x 4/5 = 36°C

Sum of 11 numbers = 36 x 11 = 396
Sum of 9 numbers = 34 x 9 = 306
Sum of remaining two numbers =396 - 306 = 90
? The smaller number = (2 x 90)/(2 + 3) = 180/5 = 36

Let the 5 consecutive positive integers be x + 1, x + 3, x + 5, x + 7, x + 9
Average = (Sum of all terms) / (Number of terms)
⇒ 9 = [(x + 1) + (x + 3) + (x + 5) + (x + 7) + (x + 9)]/5
⇒ 9 = (5x +25)/5
⇒ 45 = 5x + 25
⇒ 5x = 45 - 25
∴ 5x = 20 ⇒ x = 4
The least one is x + 1 = 4 + 1 = 5