CTET Maths MCQ - Time and Work

31 Two runners run in the same direction along a circular track 2 km long. The faster runner overtakes the slower one every 30 minutes. What are their speeds, if faster one completes a round one minute sooner than the other?

Let n₁ and n₂ be the speeds in km/hr and let n_j be the greater speed i.e., n₁ > n₂

⇒ n₁ - n₂ = 4
⇒ n₁ = 4 + n₂
⇒ n₂(4 + n₂)= 120 x 4
⇒ n₂² + 4n₂ - 480 = 0
⇒ n₂ = 20 or -24 (rejected)
∴ n₁ = 4 + n₂ = 24km/hr
Hence speeds are 24 km/hr and 20 km/hr
Alternatively
Options may also be substituted to find the result.

32 The work done by a man, a woman and a child is in the ratio of 3: 2: 1. There are 20 men, 30 women and 36 children in a factory. Their weekly wages amount of Rs. 780, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women and 30 children for 2 weeks?

	Men	Women	Children
Work	3	2	1
Numbers	20	30	36

Ratio of wages = (3 x 20) : (2 x 30) : (1 x 36)
= 5: 5: 3
Total wages of 20 men = 5/13 =Rs.300
∴ Wages of a man = Rs.15.
Similarly, wages of 30 women (5/30) x 780 = Rs.300
Wages of a woman = Rs.10
and wages of 36 children (3/13) x 780 = Rs.180
Wages of a child = Rs.5
∴ Total wages of 15 men, 21 women and 30 children
= 15 x 15 + 21 x 10 + 30 x 5
= Rs.585
∴ Total wages for 2 weeks = Rs.1170.

33 A can do a work in 6 days and B in 8 days. With the help of a boy, the three complete the work in 3 days and get Rs.200. What is the boy's share, if the money is distributed in the ratio of the work done?

Work done by A in 3 days = 3 x (1/6) = 1/2 of the work
Work done by B in 3 days = 3 x (1/8) = 3/8 of the work
∴ Work done by the boy in 3 days

= Rs. 25

34 To do certain work alone 'A' takes 4 hrs, 'B' takes 5 hrs and 'C' takes 6 hrs. How long would A and B together take to do a work which C can do in

hrs?

35 A can do piece of work in 8 days which B and C can do in 12 and 16 days respectively. If they work on alternate days, then which of the following is true?

I. Work done by A, Band C together in 3 days

work is
left of which A will finish 6/48 th of work on
10th day and B will finish remaining work on 11th day.
Thus, I is false

II. Work done by A, B, C together in 9 days = 39/48
Work left = 1 - (39/48) = 9/48 th of the whole.
On the 10th day B will finish 1/12 th of the whole.
∴ work left = (9/48) - (1/12) = 5/48 th of the whole.
On 11th day C will finish 1/16 th of the work
∴ work left = (5/48) - (1/16) = 2/48 th of the whole which will be done by A on the 12th day.
Thus, work will be finished on the 12th day.
Thus, II is false.

III. Work done by A, Band C in 9 days = 39/48
Work left after 9 days = 1 - (39/48) = 9/48 th of the whole
On the tenth day 1/16 th will be finished by C.
∴ work left = (9/48) - (1/16) = 6/48 th of the whole, which will be finished by A on the eleventh day.
Thus, III is true.