time and work Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Question :1

Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is

Answer: (c)

time-and-work-aptitude-mcq

Shortest Distance, BC = $√{5^2 + 12^2}$ = 13 km

Question :2

A, B and C together earn Rs. 300 per day, while A and C together earn Rs. 188 and B and C together earn Rs. 152. The daily earning of C is:

Answer: (c)

B's daily earning = Rs. (300 – 188) = Rs. 112.

A's daily earning = Rs. (300 – 152) = Rs. 148.

C's daily earning = Rs. [300 – (112 + 148)] = Rs. 40

Question :3

A thief steals a car at 2 : 30 p.m. and drives it at 60 kmph. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 kmph. When will he overtake the thief ?

Answer: (b)

Here, distance to be covered by the thief and by the owner is same.

Let after 2 : 30 p. m., owner catches the thief in t hrs.

Then, 60 × t = 75 $(t - 1/2)⇒t = 5/2$hrs

So, the thief is overtaken at 5 p.m.

Question :4

Pipe A can fill a tank in 10 min and pipe B can empty it in 15 min. If both the pipes are opened in an empty tank, the time taken to make it full is

Answer: (a)

Part filled by pipe A in 1 min = $1/{10}$

Part empty by pipe B in 1 min = $1/{15}$

∴ Total tank filled in minutes

= $1/{10} - 1/{15} - {3 - 2}/{30} = 1/{30}$

Hence, the tank will be filled in 30 min.

Question :5

A tyre has two punctures. The first puncture along would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

Answer: (b)

1 minute's work of both the punctures = $(1/9 + 1/6) = 5/{18}$

So, both the punctures will make the tyre flat in ${18}/5 = 3 3/5$ minutes

Alternate Method :-

both the Punctures will make the tyre flat in

$({6 × 9}/{6 + 9}) = {54}/{15} = 3 3/5$minutes

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