6. 3 adults take 2 working days to dig a trench. 4 boys can dig the same trench in thrice the time taken by these 3 adults. How many days will 8 adults and 8 boys working together take to dig the same trench?
c. 1.5 Days
d. 2 days
Explanation:
4 boys take thrice the time taken by 3 adults. So, they take 6 days.
7. Two friends P & Q take a project and start working on it together. P alone can finish the project in 20 days while Q takes 5 days more than P to finish it. After working together on the project for some days, P has to leave. Q now takes 10 days to finish the remaining project alone. After how many days of working together did P leave?
a. 5 Days
Explanation:
As seen above, Q works alone for 10 days.
Total Work done = Total days x Work done by all in 1 day
Let P and Q work together for total K days.
8. If M is asked to work alone on a project, he will require 25 days extra to finish it than the time M and N take to finish it together. However, if N is asked to finish it alone, he will require 1 week and 2 days more to finish it than what M and N would take together. In how many days will M and N finish the project working together?
a. 15 days
b. 18 days
c. 20 days
d. 25 days
∴ X = 25 x 9 = 15 days = Number of days in which M and N together finish the work
9. Working 8 hours a day, A can finish an assignment in 12 days while B takes 2 days less to finish it, working 2 hours more than A, every day. The contractor decides to put them to work together on the assignment,. Each working day now is 8 hours. How many days will they take to finish the assignment?
d. 8 days
Explanation:
A completes the work in 12 days at 8 hour per day = 12 x 8 = 96 hours
B completes the work in 8 days (2 days less than A) working 10 hours everyday (i.e. 2 hours more than A per day) = 8 x 10 = 80 hours
10. Working alone, Ram can erect the boundary wall of a land in 16 days but Samar can do the same work in 12 days. Ram and Samar are put to work on that contract on alternate days. In how many days will the boundary wall be ready, if Ram works on first day?
c. 12.5 days
Explanation:
This sum is very easy to understand and solve
First day Ram works and Second day Samar.
This means that Samar completes remaining work in 3/4th day.
| a. | 3 | Days |
| 5 |
| b. | 3 | Days |
| 4 |
d. 2 days
| Answer: a. | 3 | Days |
| 5 |
Explanation:
| In 1 day 3 adults do | 1 | amount of work ; So, in 1 day, 1 adult does | 1/2 | = | 1 | work |
| 2 | 3 | 6 |
| In 1 day, 8 adults do | 1 | x 8 = | 4 | amount of work |
| 6 | 3 |
| In 1 day 4 boys do | 1 | amount of work; So, in 1 day, 1 boy does | 1/6 | = | 1 | work |
| 6 | 4 | 24 |
| In 1 day, 8 boys do | 1 | x 8 = | 1 | amount of work |
| 24 | 3 |
| In 1 day, 8 adults and 8 boys do | 4 | + | 1 | = | 5 | amount of work |
| 3 | 3 | 3 |
| ∴ 8 adults and 8 boys together complete the entire work in | 3 | days. |
| 5 |
7. Two friends P & Q take a project and start working on it together. P alone can finish the project in 20 days while Q takes 5 days more than P to finish it. After working together on the project for some days, P has to leave. Q now takes 10 days to finish the remaining project alone. After how many days of working together did P leave?
a. 5 Days
| b. 6 | 2 | Days |
| 3 |
| c. 8 | 1 | Days |
| 5 |
| d. 10 | 2 | Days |
| 5 |
| Answer: b. 6 | 2 | Days |
| 3 |
Explanation:
Tip:
Understanding and solving such problems is very easy by drawing a line.
| In 1 day P does | 1 | work; And in 1 day Q does | 1 | work |
| 20 | 25 |
| In 10 days Q completes | 1 | x 10 = | 2 | work |
| 25 | 5 |
| Remaining work = 1 - | 2 | = | 3 | = Done by P and Q together |
| 5 | 5 |
Let P and Q work together for total K days.
| ∴ | 3 | = K x ( | 1 | + | 1 | ) |
| 5 | 20 | 25 |
| ∴ K = | 20 | = 6 | 2 | days = Days when P and Q worked together |
| 3 | 3 |
| Thus P leaves after 6 | 2 | days. |
| 3 |
8. If M is asked to work alone on a project, he will require 25 days extra to finish it than the time M and N take to finish it together. However, if N is asked to finish it alone, he will require 1 week and 2 days more to finish it than what M and N would take together. In how many days will M and N finish the project working together?
a. 15 days
b. 18 days
c. 20 days
d. 25 days
Answer: a. 15 days
Explanation:
Let M and N together finish the work in 'X' days.
So, M when working alone takes 25 days more to complete the entire work.
And, N when working alone takes 1 week and 2 days (i.e.) 9 days more to complete the entire work.
Tip: In such cases, use the following trick -
X = Extra days of P x Extra days of Q
∴ X = 25 x 9 = 15 days = Number of days in which M and N together finish the work
9. Working 8 hours a day, A can finish an assignment in 12 days while B takes 2 days less to finish it, working 2 hours more than A, every day. The contractor decides to put them to work together on the assignment,. Each working day now is 8 hours. How many days will they take to finish the assignment?
| b. | 60 | days |
| 11 |
| c. | 39 | days |
| 12 |
| d. | 15 | days |
| 8 |
| Answer: b. | 60 | days |
| 11 |
Explanation:
A completes the work in 12 days at 8 hour per day = 12 x 8 = 96 hours
| In 1 hour, A completes | 1 | amount of work |
| 96 |
| In 1 hour, B completes | 1 | amount of work |
| 80 |
| Working together, in 1 hour A and B complete | 1 | + | 1 | = | 11 | amount of work |
| 96 | 80 | 480 |
| So they complete entire work in | 480 | hours. |
| 11 |
| Since they work for 8 hours per day, they need | 480 | x | 1 | = | 60 | days |
| 11 | 8 | 11 |
10. Working alone, Ram can erect the boundary wall of a land in 16 days but Samar can do the same work in 12 days. Ram and Samar are put to work on that contract on alternate days. In how many days will the boundary wall be ready, if Ram works on first day?
| a. | 24 | days |
| 7 |
| b. | 48 | days |
| 7 |
| d. 13 | 3 | days |
| 4 |
| Answer: d. 13 | 3 | days |
| 4 |
Explanation:
This sum is very easy to understand and solve
| In 1 day Ram does | 1 | amount of work |
| 16 |
| In 1 day Samar does | 1 | amount of work |
| 12 |
| So in 2 days, Work done = | 1 | + | 1 | = | 7 | amount of work |
| 16 | 12 | 48 |
| So in 12 days (i.e. 6 times 2days) work done = 6 x | 7 | = | 42 | = | 7 |
| 48 | 48 | 8 |
| Remaining work = | 1 |
| 8 |
| Now, on 13th day, Ram will work and complete | 1 | amount of work |
| 16 |
| Now, work remaining = | 1 | - | 1 | = | 1 |
| 8 | 16 | 16 |
| We know that in 1 day Samar will complete | 1 | amount of work |
| 12 |
| 1 | > | 1 |
| 12 | 16 |
| So, how long would Samar take to finish | 1 | of work? |
| 16 |
| = | 1 | ÷ | 1 | = | 3 |
| 16 | 12 | 4 |
| So answer is 13 + | 3 | days = 13 | 3 | days |
| 4 | 4 |
