Time and Distance and Time and work (UPSC) Part-II

Total Questions: 32

21. A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

(a) 1 : 2
(a) 1 : 2
(c) 1 : 3
(d) 3 : 1

Correct Answer: (d) 3 : 1

Solution:Let speed in still water is u km/hr. and speed of current is v km/hr.
Downstream speed = (u + v) km/hr.
Upstream speed = (u - v) km/hr.

Time to row upstream (t₁) = d / (u - v)
where d = distance to row
Time to row downstream (t₂) = d / (u + v)
ATQ,

t₁/t₂ = 2/1 ⇒ d / (u - v) / d / (u + v)
⇒ (u + v) / (u - v) = 2/1

⇒ (u/v + 1) / (u/v - 1) = 2 ⇒ (u/v) = 3 ∴ u : v = 3 : 1.

22. A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1°5 km/hr and Y walks with a uniform speed of 1 in the first hour, with a uniform speed of 1·25 km/hr in the second hour and with a uniform speed of 1·5 km/hr in the third hour and so on. [2020-II]

Which of the following is/are correct ?

They take 5 hours to meet.
They meet midway between A and B.

Select the correct answer using the code given below :

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor

Correct Answer: (c) Both 1 and 2

Solution:Distance between places A and B = 15 km
Speed of X = 1.5 km/hr
So, Distance covered by X in 5 hours = 7.5 km
Speed of Y in 1st hour = 1 km/hr
So, Distance covered by Y in 1st hour = 1 km
Similarly, Distance covered by Y in 2nd hour = 1.25 km
Distance covered by Y in 3rd hour = 1.5 km
Distance covered by Y in 4th hour = 1.75 km
Distance covered by Y in 5th hour = 2 km
So, the total distance covered by Y in 5 hours = 1 + 1.25 + 1.5
+ 1.75 + 2 = 7.5 km
Hence, both the given statements are true.

23. Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?

Distance between X and Y = 40 + 60 = 100m

(a) 100 m
(b) 90 m
(c) 60 m
(d) 50

Correct Answer: (a) 100 m

Solution:Distance between X and Y = 40 + 60 = 100 m

24. X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)? [2022-II]

(a) 2
(b) 3
(c) 4
(d) 5

Correct Answer: (b) 3

Solution:Number of round = 3 × 1000 / 300 = 10 round

And, L.C.M of speed 3 and 2 = 6
Thus, X meets Y after every 3 rounds
Hence, number of times X crosses Y in 10 rounds
= 10 / 3 = 3 times

25. 24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work? [2022-II]

(a) 30 days
(b) More than 30 days
(c) Less than 30 days or more than 30 days
(d) Data is inadequate to draw any conclusion

Correct Answer: (d) Data is inadequate to draw any conclusion

Solution:24 men + 12 Women = 30 days work
∴ 2 men + 1 women = 30 × 12 days work.
⇒ 12 men + 6 women = 30 × 2 days work.
⇒ 48 men + 24 women = 30 / 2 days work.

But we still need some information to solve this question.

26. A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. [2023-II]

Consider the following statements :

The work will be finished on Thursday.
The work will be finished in 10 days.
Which of the above statements is/are correct ?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (a) 1 only

Solution:L.C.M. of 8, 16 and 12 = 48 units

Work done/day by A = 48 / 8 = 6 units

Work done/day by B = 48 / 16 = 3 units

Work done/day by C = 48 / 12 = 4 units

Work done in 3 consecutive days = 6 + 3 + 4 = 13 unit

Time required to complete 39 units work = 39 / 13 × 3 = 9 days

Work finished on 11ᵗʰ day = 39 + 6 + 3 = 48 units
Hence, on 11ᵗʰ day, whole work is finished and 11ᵗʰ day after
monday will be thursday.

27. Consider the following: [2024-II]

Weight of 6 boys = Weight of 7 girls = Weight of 3 men
= Weight of 4 women
If the average weight of the women is 63 kg, then what is the
average weight of the boys?

(a) 40 kg
(b) 42 kg
(c) 45 kg
(d) 63 kg

Correct Answer: (b) 42 kg

Solution:Weight of 6 boys = 7 girls = 3 Men = 4 Women = W (says)
∴ Average weight of women = W/4 = 63 (given)
∴ W = 63 × 4.
Now, weight of 6 boys = 63 × 4
∴ Average weight of a boy = 63 × 4 / 6 = 42 kg

28. How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)? [2024-II]

(a) 3 times
(b) 4 times
(c) 5 times
(d) 6 times

Correct Answer: (a) 3 times

Solution:Two hand of the clock meet one time between 10 AM to 11 AM and between 11 AM to 1 PM two hand meet only one time at sharp 12’O clock.
Two hand of the clock meet one more between 1 PM to 2 PM
Hence, total number of times = 1 + 1 + 1 = 3

29. Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹ 400 more than Q’s share out of the total profit of ₹ 2,000, what is the capital contributed by P? [2024-II]

(a) ₹ 30,000
(b) ₹ 26,000
(c) ₹ 24,000
(d) ₹ 20,000

Correct Answer: (a) ₹ 30,000

Solution:Let P’s investment = (X + 14000) and Q’s investment = X.
As profit is divided into investment X time.
Now, Ratio = (14000 + x) × 8 : 10 x.
4 (14000 + x) : 5x
Again, P’s profit = 400 + Q’s profit
2000 = (Q + P) is profit
2000 = Q + 400 + Q ⇒ Q’s profit = 800.
and P’s profit = 800 + 400 = 1200.
Now, (14000 + x) × 8 / 10x = 1200 / 800
8x + 112000 = 15x

7x = 112000.
∴ x = 16000.
∴ P’s investment = 16000 + 14000 = 30000.

30. A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days? [2024-II]

(a) 10%
(b) (50/3)%
(c) 20%
(d) 25%

Correct Answer: (c) 20%

Solution:Let n men complete work in 6k day.
and m men complete same work in 5k day
∴ 6k n = 5 km.

m = 6/5 n = 1.2n

∴ Required % = (m - n)/n × 100 = (1.2n - n)/n × 100 = 20%

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