## Answer Key of Time & Work MCQ Quiz 1

# We provide a answer key of Time Work MCQ Quiz 1 which has been published in head of Banking/Competitive exam mcq. Following are the questions and their detail explanation of answers.

# Q.1. 3 workers Peroola, Rahul and Prashant can complete a piece of work in 6 days. Peroola takes 15 days less than Rahul to complete the same work. Find in how many days will Prashant complete the whole work alone with 75% of his original efficiency, if Rahul can complete the work alone in 35 days?

A.
56037 days

B.
49936 days

C.
36117 days

D.
55543 days

Answer

Ø Peroola + Rahul
+ Prashant = 6

Ø Rahul = 35

Ø Peroola = (35 –
15) = 20

Ø Total units of
work = 420

Ø (Peroola + Rahul
+ Prashant)’s one day work = 70 units

Ø Peroola’s one
day work = 21 units ⇒ Rahul = 12 units

Ø Prashant’s one
day work = 70 – 33 = 37 units

Ø Prashant’s
efficiency to do the work alone = 75/100 × 37

Ø Time required to
complete the work = 420x 4/37x3 = 560 / 37 Days

Ø **Hence, option A is correct.**

### Q.2. Three persons A , B, and C complete a piece of work in 6 days for which they are paid a sum of Rs. 480.If the efficiency of A, B and C are in ratio 4 : 5 :7, then find the daily income of B?

A.
Rs. 25

B.
Rs. 30

C.
Rs. 150

D.
Rs. 20

Answer:-

Ø Total amount earned by A ,B, and C in 6 days =Rs 480

Ø The amount earned by them in 1 day = 480/6= Rs 80

Ø Amount of money earned is proportional to the amount of work done

Ø Let work done by A ,B and C be 4x, 5x and 7x.

Ø ∴ Total work done by A,B and C together= 16x

Ø Work done by B = 5x

Ø Daily income of B = 5x/16x X 80= Rs. 25

Ø

Hence, option A is correct.

### Q.3. Rashmi and Pallavi can make a carpet in 3 days and 12 days more than the time taken if both of them worked together. Find the time in which Rashmi can make the carpet alone.

A.
9 days

B.
6 days

C.
12 days

D.
8 days

Answer:-

Ø Let the time both of them together will take to make the carpet be x days

Ø Time taken by Rashmi alone = x + 3 days

Ø Time taken by Pallavi alone = x + 12 days

Ø One day work when they both work together = Sum of their individual per day work

Ø 1/x = 1/x+12 + 1/x+3

Ø 1/x = 2x + 15/ x

^{2 }+15x+36= 2x^{2}+15xØ x =6

Ø Time taken by Rashmi to make carpet alone = 6 + 3 = 9 days

Ø

Hence, option A is correct.

### Q.4. Three workers Trump, Putin and Jinping are appointed to do a job. They together started the job but Jinping left after 3 days when 37% of the job was done. The remaining job was completed by Trump and Putin in 7 days. The ratio of efficiency of Trump and Putin is 4 : 5. Find the number of days required by the slowest worker to complete the entire job alone?

A.
22 days

B.
20 days

C.
24 days

D.
30 days

Answer:-

Ø Let x, y and z are the one day’s work of Trump, Putin and Jinping respectively.

Ø According to the question,

Ø ⇒ 3 × (x + y + z) = 37% of the work

Ø ⇒ 7 × (x + y) = 63%

Ø ⇒ x + y = 9%

Ø ∵ The ratio of efficiency of Trump and Putin is 4 : 5,

Ø ∴ 5x = 4y and x = 4%, y = 5% work per day.

Ø It implies Trump can complete the job and in 25 days and Putin in 20 days.

Ø In 3 days (x + y + z) do 37% of the work

Ø Out of this Trump and Putin would do 27% work = (3 × 9%) of the work.

Ø Remaining work = 37% – 27% = 10% (done by Jinping in 3 days)

Ø ∴ The work of z =10/3 = 3.33% work per day

Ø ∴ Jinping is the slowest and he would do the work in 30 days.

Ø

Hence, option D is correct.

### Q.5. A group of men decided to do a job in 4 days, but 20 men dropped out everyday. Find the number of men who initially decided to do the job, if job was completed in 7 days?

A.
70

B.
110

C.
140

D.
120

Anwer:-

Ø Let the initial number of men be m

Ø Total work = 4 m

Ø m + (m – 20) + (m – 40) + …… = 4 m

Ø 7/2 [2m + 6 (–20)] = 4m

Ø 7/2 (2m – 120) = 4m

Ø m =140

Ø

Hence, option C is correct.

### Q.6. Two male workers A and B can complete a piece of work in 20 and 35 hours respectively. A female worker, C can complete the whole work alone in H hours with three - fourth of her original efficiency. If all the three working together with their usual efficiency can complete the whole work in 6 hours, then find the value of H.

A.
460/37 days

B.
560/27 days

C.
460/17 days

D.
560/37 days

Answer:-

Ø Total units of work = 420

Ø (A + B + C)’s one hour’s work = 70 units

Ø A’s one hour’s work = 21

Ø units ⇒ B = 12 units

Ø C’s one hour’s work = 70 – 33 = 37 units

Ø C’s efficiency to do the work alone = 3×37/4

Ø ∴ Time reqd. to complete the work = 420 × /37 ×3 =560/37 hours

Ø

Hence, option D is correct.

### Q.7. Raj can do a piece of work in 20 days and Rohan can do it in 12 days. On which date will they complete the work, if they work together on prime number dates starting on 29th April?

A.
7th May

B.
17th May

C.
13th May

D.
23rd May

Answer:-

Ø Total work = 60 {LCM of 20, 12}

Ø A/day = 3; B/day = 5; together = 8/ days = No. of days = 7.5 days

Ø 8th prime number date starting from 29th April

Ø 29th April, 2nd May, 3rd May, 5th May, 7th May, 11th May, 13th May, 17th May

Ø

Hence, option B is correct.

### Q.8. To do a certain task Bhuvan would take 3 times as long as Abir and Varun together; and Varun would takes 4 times as long as Abir and Bhuvan together. Three of them together can complete the task in 5 days. How much time is taken by Bhuvan and varun to complete the task?

A.
14x1/2 days

B.
13x1/3 days

C.
12 days

D.
11x1/9 days

Answer:-

Ø Let us represent efficiency of Abir, Bhuvan and Varun by A, B and V respectively.

Ø According to the question,

Ø B/A+V =1/3………..(1)

Ø V/A+B = 1/4……….(2)

Ø To equate the ratio in the above equations, let us multiply (1) by 5 and (2) by 4.

Ø So, A : B : V = 11 : 5 : 4

Ø 11 + 5 + 4 = 20 units

Ø In 5 days, task completed = 20 × 5 = 100 units (total task)

Ø Time taken by Bhuvan and Varun to complete the task

Ø = 100/4+5 = 11x1/9 days

Ø

Hence, option D is correct.

### Q.9. If 5 men and 5 women work together then they can finish a work in 5 days but if 5 women work alone then they take 40/3 more days than the time required by 5 men. Find efficiency of one woman is how much percentage less than one man?

A.
60%

B.
66.66%

C.
40%

D.
62.5%

Answer:-

Ø Let the days taken by 5W = x and 5M = y.

Ø One day work of 5W = 1/x and that of 5M = 1/ y

Ø 1/x + 1/y = 1/5

Ø 5 (x + y) = xy --------(1)

Ø x = 40/3 + y

Ø 3 (x – y) = 40 -------(2)

Ø Multiplying eq 1 and 2

Ø 3 (x² – y²) = 8xy

Ø Dividing by y²

Ø 3x

^{2}/y2 – 8x/ y-3 = 0Ø Let x/y = t

Ø 3t² – 8t – 3 =0

Ø t = 3

Ø x/y = 3/1

Ø So ratio of efficiency of W : M = 1 : 3

Ø Efficiency of Women = 66.67% less than that of Men

Ø

Hence, option B is correct.

### Q.10. A can do 3/5th of work in 15 days. Efficiency of B is 25% more than that of A. Both A and B started working together and left the work after five days. C completed the remaining work in 11 days. Efficiency of C is what percent more/less than that of A ?

A.
20% less

B.
25% more

C.
20% more

D.
25% less

Answer:-

Ø A does 3/5th of work in 15 days.

Ø Time Taken by A to complete the work

Ø = 53 × 15 = 25 days

Ø Efficiency of B is 25% more than that of A.

Ø If Work done by A in one day = 4, then work done by B in one day = 5

Ø Ratio of time taken by A and B = 5 : 4

Ø Time taken by B to complete the work

Ø = 4/5 × 25 = 20 days 5

Ø A and B worked for five days.

Ø Total work Completed by A and B in 5 days

Ø =5(1/25 + 1/20)

Ø = 1/5+1/4= 9/20

Ø Work Left = 11/20 which is done by C in 11 days.

Ø Time taken by C to complete the whole work = 20/11 × 11

Ø C = 20 days

Ø Ratio of Efficiency of A and C = 20/25

Ø Efficiency of C is 25 % more than that of A.

Ø

Hence, option B is correct.

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