Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of the train during the whole journey.
Answer : Option B
Sol. Required average speed = `((2xy)/(x + y))` km/hr
= `(2 xx 84 xx 56)/(84 + 56)` km/hr
=` ((2 xx 84 xx 56)/(140))` m/hr = 67.2 km/hr.
A batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . Find his average after 17th inning.
Answer : Option C
Sol. Let the average after 17th inning = `x`
Then , average after 16th inning = `(x - 3)`
`:.` ` 16 (x - 3) + 87 = 17 x`
or `x = (87 - 48) = 39.`
There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Re. 1 What was the original expenditure of the mess ?
Answer : Option A
Sol. Let the original average expenditure be Rs. `x` , Then
42(`x` - 1) - 35`x` = 42
`hArr 7x = 84`
`rArr x = 12.`
`:.` Original expenditure = Rs. (35 x 12) = Rs. 420.
The average weight of 10 oarsmen in a boat is increased by 1.8 kg When one of the crew, who weights 53 kg is replaced by a new man. Find the weight of the new man .
Answer : Option C
Sol. Total weight increased = (1.8 x 10) kg = 18 kg.
`:.` Weight of the new man = (53 + 18) kg = 71 kg.
The average age of a class of 39 students is 15 years . If the age of the teacher be included, then the average increases by 3 months. Find the age of he teacher..
Answer : Option D
Sol. Total age of 39 persons = (39 x 15) years = 585 years.
Average age of 40 persons = 15 years 3 months = ` 61/4 ` years.
Total age of 40 persons = `(61/4 xx 40)` years = 610 years.
`:.` Age of the teacher = (610 - 585) years = 25 years.