31. The average age of an adult class is 40 years. 12 new students with an average of 32 years join the class, thereby decreasing the average by 4 years. The original strength of the class was :
a. 10
b. 11
c. 12
d. 15
Answer: C
Explanation:
Let original strength = x, Then,
40x + 12 $ \times $32=(x+12)$ \times $36
or 40x + 384 = 36x + 432 or
4x = 48 or x = 12
32. The average of 6 observations is 12. A new seventh observation is included and the new average is decreased by 1. The seventh observation is :
a. 1
b. 3
c. 5
d. 6
33. Out of four numbers, the average of first three is 15 and that of the last three is 16. If the last number is 19, the first is :
a. 15
b. 16
c. 18
d. 19
Answer: B
Explanation:
Sum of four numbers = (15$ \times $3 + 19)= 64
Sum of last three numbers = (16$ \times $3) = 48
First number = (64 - 48) = 16
34. The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average one number, namely 36 was wrongly read as 26. The correct average is :
a. 12.4
b. 14
c. 16
d. 18.6
Answer: C
Explanation:
Sum of numbers = (10$ \times $15 - 26 + 36)=160
Correct average = ${\displaystyle\frac{{160}}{{10}} = 16}$
35. The average of 25 results is 18, that of first twelve is 14 and of last twelve is 17. Thirteenth result is :
a. 28
b. 72
c. 78
d. 85
Answer: C
Explanation:
Thirteenth result =(25$ \times $18-12$ \times $14+12$ \times $17)=78
36. A man goes to a place at the rate of 4 kmph. He comes back on a bicycle at 16 kmph. His average speed for the entire journey is :
a. 5 km/hr
b. 6.4 km/hr
c. 8.5 km/hr
d. 10 km/hr.