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Time and Work Exercise 3

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  1. Question 1 of 18
    1. Question

    After working for 8 days, Anil finds that only ⅓ of the work has been done. He employs Rakesh who is 60 % efficient as Anil. How many more days will they take to complete the job?

    Hint

    In 8 days, Anil does = ⅓rd work.

    ∴ in 1 day, he does = ¹⁄₂₄th work

    ∴ Rakesh’s one day’s work

    = 60% of ¹⁄₂₄ = ¹⁄₄₀ th work.

    Remaining work

    time-and-work-q-65859.png

    (Anil and Rakesh)’s one day’s work

    = time-and-work-q-65853.png

    = ¹⁄₁₅th work

    Now, ¹⁄₁₅th work is done by them in one day.

    ∴ ⅔rd work is done by them in 15 × ⅔ = 10 days

  2. Question 2 of 18
    2. Question

    A sum of Rs. 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days. How much did C receive if all the four work together?

    Hint

    A’s one day’s work = ¹⁄₃₂

    B’s one day’s work = ¹⁄₂₀

    (B + C)’s one day’s work =¹⁄₁₂

    ∴ C’s one day’s work

    = time-and-work-q-65847.png

    D’s one day’s work = ¹⁄₂₄

    ∴ (A + B + C + D)’s one day’s work

    = time-and-work-q-65841.png

    time-and-work-q-65835.png

    = time-and-work-q-65828.png

    ∴ Out of ⁵⁄₃₂ of work done, ¹⁄₃₀ of the work is done by C.

    ⇒ Out of Rs. 25 paid for the work, C will receive

    Rs. time-and-work-q-65822.png

    i.e. time-and-work-q-65816.png

    i.e. Rs.¹⁶⁄₃

  3. Question 3 of 18
    3. Question

    A and B can do a job in 15 days and 10 days, respectively. They began the work together but A leaves after some days and B finished the remaining job in 5 days. After how many days did A leave?

    Hint

    A’s one day’s work = ¹⁄₁₅th work.

    B’s one day’s work = ¹⁄₁₀th work.

    (A + B)’s one day’s work

    time-and-work-q-65810.pngwork.

    Let A left after x days.

    ∴ (A +B)’s x days’ work = ¹⁄₆th work.

    Remaining work

    time-and-work-q-65804.png work.

    Now, in 5 days, work done by

    time-and-work-q-65798.png.

    ∴ In 1 day work done by B

    time-and-work-q-65792.png

    and time-and-work-q-65786.png

    ∴ x = 3 days

  4. Question 4 of 18
    4. Question

    Mr. Suresh is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Suresh’s tour programme is :

    Hint

    Let Suresh undertakes a tour of x days.

    Then, expenses for each day = 360/x

    Now, time-and-work-q-65780.png

    ⇒ time-and-work-q-65774.png = 3

    ⇒ x² + 4x – 480 = 0

    ⇒ x = – 24 or x = 20

    Since, x ≠ -24 we have x = 20

  5. Question 5 of 18
    5. Question

    A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, then in how many days would each of them take alone to finish it?

    Hint

    Let B can finish the work in x days.

    Then A can finish the work in (x – 3) days.

    B’s one day’s work time-and-work-q-65768.png

    A’s one day’s work time-and-work-q-65762.png work

    A’s 4 days’ work = time-and-work-q-65756.png

    Remaining work

    time-and-work-q-65749.png

    The remaining work done by B in 14 – 4

    = 10 days.

    Now, in 10 days, work done by

    time-and-work-q-65743.png th work

    ∴ In 1 day, work done by B

    = time-and-work-q-65737.png work

    and time-and-work-q-65731.png

    ⇒ x = 15 days

    ∴ B will finish in 15 days and A will finish in 12 days

  6. Question 6 of 18
    6. Question

    Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked ⅓ as efficiently as he actually did, the work would have completed in 3 days. Find the time for A to complete the job alone.

    Hint

    (A + B)’s one day’s work = ⅕th work

    Let A can do job in x days. Then,

    A’s one day’s work

    time-and-work-q-65725.png

    and B’s one day’s work

    time-and-work-q-65719.png

    time-and-work-q-65713.png

    Now , time-and-work-q-65707.png

    time-and-work-q-65701.png

    time-and-work-q-65695.png

  7. Question 7 of 18
    7. Question

    If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

    Hint

    Let 1 man’s 1 day’s work = x and

    1 boy’s 1 day’s work = y.

    Then, 6x + 8y = ¹⁄₁₀

    and 26x + 48y = ½

    Solving these two equations, we get :

    time-and-work-q-65689.png

    ∴ (15 men + 20 boys)’s 1 day’s work

    = time-and-work-q-65683.png

    ∴ 15 men and 20 boys can do the work in 4 days.

  8. Question 8 of 18
    8. Question

    39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

    Hint

    Let the required number of days be x.

    Less persons, More days (Indirect Proportion)

    More working hrs per day, Less days (Indirect Proportion)

    time-and-work-q-70683.png

    time-and-work-q-70676.png

  9. Question 9 of 18
    9. Question

    A certain number of persons can dig a trench 100 m long, 50 m broad and 10 m deep in 10 days. The same number of persons can dig another trench 20 m broad and 15 m deep in 30 days. The length of the second trench is :

    Hint

    Let the required length be x metres.

    More breadth, Less length (Indirect Proportion)

    More depth, Less length (Indirect Proportion)

    More days, More length (Direct Proportion)

    time-and-work-q-70670.png

    ∴ 20 × 15 × 10 × x = 50 × 10 × 30 × 100

    time-and-work-q-70664.png

  10. Question 10 of 18
    10. Question

    If 8 men or 17 boys can do a piece of work in 26 days, how many days will it take for 4 men and 24 boys to do a piece of work 50 × 0.9 times as great?

    Hint

    Let the required number of days be x.

    8 men = 17 boys

    ⇒ 4 men time-and-work-q-70658.png

    ∴ 4 men and 24 boys

    time-and-work-q-70652.png

    Now, More boys , less days (Indirect Proportion)

    time-and-work-q-70646.png

    time-and-work-q-70640.png

    time-and-work-q-70634.png

    But work → 50 × 0.9 times

    ∴ Required days

    time-and-work-q-70628.png

  11. Question 11 of 18
    11. Question

    If 18 men working 5 hours a day for 8 days can complete a job, how many men working 8 hours a day for 6 days will be needed?

    Hint

    Let the required men be x.

    More hours, less men (Indirect proportion)

    More days, less men (Indirect proportion)

    time-and-work-q-70622.png

    ∴ 5 × 8 × 18 = 8 × 6 × x

    time-and-work-q-70616.png

  12. Question 12 of 18
    12. Question

    4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

    Hint

    Let the required number of mats be x.

    More weavers, More mats (Direct Proportion)

    More days, More mats (Direct Proportion)

    time-and-work-q-70609.png

    time-and-work-q-70603.png

  13. Question 13 of 18
    13. Question

    In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

    Hint

    Let the required number of days be x.

    Less cows, More days (Indirect Proportion)

    Less bags, Less days (Direct Proportion)

    time-and-work-q-70597.png

    ∴ 1 × 40 × x = 40 × 1 × 40

    ⇒ x = 40

  14. Question 14 of 18
    14. Question

    Two coal loading machines each working 12 hours per day for 8 days handles 9,000 tonnes of coal with an efficiency of 90%. While 3 other coal loading machines at an efficiency of 80% set to handle 12,000 tonnes of coal in 6 days. Find how many hours per day each should work.

    Hint

    More machines, less hours (Indirect Proportion)

    Less days, more hours (Indirect Proportion)

    More amount of coal, more hours (Direct Proportion)

    Less efficiency, more hours (Indirect Proportion)

    time-and-work-q-70591.png

    ⇒ 3 × 6 × 9,000 × 0.8 × x

    = 2 × 8 × 12,000 × 0.9× 12

    ⇒ x = 16 hrs

  15. Question 15 of 18
    15. Question

    A man and a boy together can do a certain amount of digging in 40 days. Their skills in digging are in the ratio of 8 : 5. How many days will the boy take, if engaged alone.

    Hint

    Let M denotes man and B denotes boy.

    (M + B)’s 1 day’s work = ¹⁄₄₀

    i.e. time-and-work-q-70585.png

    Ratio of their skill = ⁸⁄₅

    i.e. time-and-work-q-70579.png

    Let efficiency of a man of 1 days work = x

    i.e. time-and-work-q-70573.png

    Now, time-and-work-q-70567.png

    Now, time-and-work-q-70561.png

    ⇒ M = 65 and time-and-work-q-70555.png

  16. Question 16 of 18
    16. Question

    A contractor undertakes to do a piece of work in 40 days. He engages 100 men and after 35 days, he engaged an additional 100 men and completes the work. How many days behind the schedule would the work have been, if he had not engaged the additional men?

    Hint

    (100 × 35+ 200 × 5) men can finish the work in 1 day.

    i.e., 4500 men can finish the work in 1 day

    ∴ 100 men can finish the work in 45 days

    ∴ The work would be 5 days behind the schedule.

  17. Question 17 of 18
    17. Question

    A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, ⅖ of the work is finished. How many additional men may be employed so that work may be completed on time, each man now working 9 hours per day?

    Hint

    Remaining work time-and-work-q-70549.png

    Remaining time = 56 – 30 = 26 days

    More work, more men (Direct Proportion)

    Less days, more men (Indirect Proportion)

    More hours, Less men (Indirect Proportion)

    time-and-work-q-70543.png

    time-and-work-q-70536.png

    ⇒ x = 160

    ∴ Additional men to be employed = 160 – 104 = 56 men

  18. Question 18 of 18
    18. Question

    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?

    Hint

    1 minute’s work of both the punctures

    = time-and-work-q-70530.png

    So, both the punctures will make the tyre flat in

    time-and-work-q-70524.png

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