WORKSHEET ON TIME AND WORK PROBLEMS

Problem 1 :

Worker A takes 8 hours to do a work. Worker B takes 10 hours to do the same work. How long will it take both A and B, working together but independently, to do the same work?

Problem 2 :

A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?

Problem 3 :

A can do a piece of work in 7 days of 9 hours each day and B can do it in 6 days of 7 hours each day. How long will it take for them to complete the work, working together 8⅖ hours a day?

Problem 4 :

A and B can do a piece of work in 18 days; B and C can do the same work in 24 days; A and C can do it 36 days. In how many days will A, B and C finish it, working together and separately?

Problem 5 :

A is twice as good as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

Problem 6 :

A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same work?

Problem 7 :

A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?

Problem 8 :

A and B undertake to do a piece of work for \$600. A alone can do it 6 days while B alone can do it in 8 days. With the help of C, they finish it ion 3 days. Find the share of each.

Problem 9 :

A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A begining, in how many days will the work be completed?

Problem 10 :

45 men can complete a work in 16 days. Six days afetr they started working, 30 more men joined them. How many days will they now take to complete the remaning work?

Problem 11 :

2 men and 3 boys can do a piece of work in 10 days, while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the same work?

A's 1 hour work =

B's 1 hour work =

(A + B)'s 1 hour work = ⅛ ⅒ ⁹⁄₄₀

Time taken by both A and B to finish the work :

⁴⁰⁄₉

= 4⁴⁄₉ hours

(A + B)'s 1 day work = ¼

A's 1 day work = ¹⁄₁₂

B's 1 day work = ¼ ¹⁄₁₂

Therefore, B alone can finsih the work in

⁶⁄₁

= 6 days

Time taken by A to complete the work :

= 7  9

= 63 hours

A's 1 hour work = ¹⁄₆₃

Time taken by B to complete the work :

= 6  7

= 42 hours

B's 1 hour work = ¹⁄₄₂

(A + B)'s 1 hour work = ¹⁄₆₃ ¹⁄₄₂ ⁵⁄₁₂₆

Time taken by both A and B to finsih the work :

= ¹²⁶⁄₅ hours

Number of days taken by both A and B to finsih the work, working 8⅖ hours a day :

¹²⁶⁄₅ ÷ 8

¹²⁶⁄₅ ÷ ⁴²⁄₅

¹²⁶⁄₅  ⁵⁄₄₂

= 3 days

(A + B)'s 1 day work = ¹⁄₁₈ ----(1)

(B + C)'s 1 day work = ¹⁄₂₄ ----(2)

(A + C)'s 1 day work = ¹⁄₃₆ ----(3)

(1) + (2) + (3) :

(A + B) + (B + C) + (A + C) = ¹⁄₁₈ + ¹⁄₂₄ ¹⁄₃₆

A + B + B + C + A + C = ⁹⁄₇₂

2A + 2B + 2C =

2(A + B + C) =

(A + B + C)'s 1 day work = ¹⁄₁₆

Number of days taken by A, B and C together to finish the work :

¹⁶⁄₁

﻿= 16 days

A's 1 day work :

= (A + B + C)'s 1 day work - (B + C)'s 1 day work

= ¹⁄₁₆ ¹⁄₂₄

¹⁄₄₈

Number of days taken by A alone to finish the work :

⁴⁸⁄₁

= 48 days

B's 1 day work :

= (A + B + C)'s 1 day work - (A + C)'s 1 day work

= ¹⁄₁₆ ¹⁄₃₆

⁵⁄₁₄₄

Number of days taken by B alone to finish the work :

¹⁴⁴⁄₅

= 28⅘ days

B's 1 day work :

= (A + B + C)'s 1 day work - (A + C)'s 1 day work

= ¹⁄₁₆ ¹⁄₃₆

⁵⁄₁₄₄

Number of days taken by B alone to finish the work :

¹⁴⁴⁄₅

= 28⅘ days

C's 1 day work :

= (A + B + C)'s 1 day work - (A + B)'s 1 day work

= ¹⁄₁₆ ¹⁄₁₈

¹⁄₁₄₄

Number of days taken by C alone to finish the work :

¹⁴⁴⁄₁

= 144 days

(A's 1 days work ) : (B's 1 day work) = 2 : 1

(A + B)'s 1 day work = ¹⁄₁₈

Divide ¹⁄₁₈ in the ratio 2 : 1.

A's 1 day work = ¹⁄₁₈ ⋅ ⅔ ¹⁄₂₇

Number of days taken by A alone to finish the work :

²⁷⁄₁

= 27 days

Ratio of times taken by A and B :

= 160 : 100

= 8 : 5

Number of days taken by A = 8x

Number of days taken by B = 5x

Given : A takes 12 days to complete the work.

8x = 12

x = 1.5

Number of days taken by B to complete the work :

= 5(1.5)

= 7.5 days

A's 1 day work = ¹⁄₈₀

Work done by A in 10 days :

= 10 ⋅ ¹⁄₈₀

¹⁄₈

Remaining work :

= 1 - ¹⁄₈

⅞ of the work done by B in 42 days.

Number of days taken by to complete the whole work :

= 42 ÷

= 42  ⁸⁄₇

= 48 days

B's 1 day work = ¹⁄₄₈

(A + B)'s 1 day work = ¹⁄₈₀ ¹⁄₄₈ ¹⁄₃₀

Number of days taken by A and B, working together :

³⁰⁄₁

= 30 days

A's 1 day work =

B's 1 day work =

(A + B + C)'s 1 day work =

C's 1 day work = ⅓ - (⅙ + ) = ¹⁄₂₄

Ratio of 1 day work :

A : B : C = ⅙ : ⅛ ¹⁄₂₄

A : B : C = 4 : 3 : 1

A's share = 4x

B's share = 3x

C's share = x

Given : The work is undertaken for \$600.

4x + 3x + x = 600

8x = 600

x = 75

Therefore,

A's share = 4(75) = \$300

B's share = 3(75) = \$225

C's share = \$75

A's 1 day work =

B's 1 day work = ¹⁄₁₂

A and B work for a day alternately and A starts on the first day. So, B works on the second day, A works on the third day and so on.

(A + B)'s 2 days work = ⅑ + ¹⁄₁₂ ⁷⁄₃₆

Work completed in the first ten days (5 pairs of days) :

= 5 ⁷⁄₃₆ ³⁵⁄₃₆

Remaning work = 1 - ³⁵⁄₃₆ ¹⁄₃₆

On 11th day, its A's turn. He can complete  of the work in one day.

Time taken by A to complete ¹⁄₃₆ of the work on 11th day :

¹⁄₃₆ ÷

¹⁄₃₆  ⁹⁄₁

= ¼ day

Total time taken to complete the work :

= (10 + ¼) days

= 10¼ days

45 men can complete the work in 16 days.

45 men's 1 day work = ¹⁄₁₆

1 man's  1 day work = ¹⁄₍₁₆₄₅₎ ¹⁄₇₂₀

45 men's 6 days work = 6 ⋅ ¹⁄₁₆

Remaning Work

This remaning ⅝ of the work is completed by 75 men.

We already know that 1 man's 1 day work is ¹⁄₇₂₀.

75 men's 1 day work = 75 ⋅ ¹⁄₇₂₀ ⁵⁄₄₈

Time taken by 75 men to complete the remanining work :

÷ ⁵⁄₄₈

⋅ ⁴⁸⁄₅

= 6 days

Let us assume x and y as follows.

1 man's 1 day work = x

1 boy's 1 day work = y

Given : 2 men and 3 boys can do the work in 10 days.

(2 men + 3 boys)'s 1 day work =

2x + 3y = ⅒ ----(1)

Given : 3 men and 2 boys can do the work in 8 days.

(3 men + 2 boys)'s 1 day work =

3x + 2y =  ----(2)

Solving (1) and (2),

x = ⁷⁄₂₀₀  and  y = ¹⁄₁₀₀

(2 men + 1 boy)'s 1 day work = 2 ⋅ ⁷⁄₂₀₀ ¹⁄₁₀₀

= ⁷⁄₁₀₀ ¹⁄₁₀₀

= ⁸⁄₁₀₀

²⁄₂₅

Number of days taken by 2 men and 1 boy to complete the work :

²⁵⁄₂

= 12½ days

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