time and work Model Questions & Answers, Practice Test for ssc chsl tier 1 2023

Question :11

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

Answer: (c)

Ratio of times taken by A and B

= 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 : : 23 : x

⇒ x=$({23×23}/10) ⇒ x={299}/10$

A's 1 day's work

= $1/{23}$; B's 1 day's work = $10/299$

(A + B)'s 1 day's work = $(1/23+10/299)=23/299=1/13$

∴ A and B together can complete the job in 13 days.

Question :12

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B.

Answer: (c)

Downstream speed = (14 + 4) km/h = 18 km/h.

Upstream speed = (14 – 4) km/h = 10 km/h.

Let the distance between A and B be d km. Then,

$d/{18} + {(d/2)}/{10} = 19⇒d/{18} + d/{20} = 19⇒{19d}/{180}$ = 19

⇒d = 180 km.

Question :13

A man started running at a distance of 225 metre from the train. If the speed of the man is 6 km/h, then how much time should the train wait so that the man will be just able to catch it ?

Answer: (a)

Time = ${225}/{6 × 5/{18}} = 135 sec = 2{1/4}$ min.

Question :14

A contractor undertook to do a piece of work in 9 days. He employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days. Find the number of men originally employed .

Answer: (a)

Let the number of men originally employed be x.

9x = 15(x – 6)

or x = 15

Question :15

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

Answer: (d)

Speed upstream = 7.5 kmph; Speed downstream = 10.5kmph.

∴ Total time taken = $({105}/{7.5} + {105}/{10.5})$ hours = 24 hours.

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