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

ssc mts tier 1 2024 SYLLABUS WISE SUBJECTS MCQs

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

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:

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 ?

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

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 ?

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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