**Question 16:**

If A and B can do a piece of work in 8 days, B and C in 12 days and C and A in 16 ‘' days, then in how many days will C finish it when working alone?

[1] 80 days

[2] 36 days

[3] 96 days

[4] 88 days

**Answer:**

**Explanation: **

(A + B)'s one day's work = 1/8, (B + C)'s one day's work = 1/12.

(A +C)'s one day's work = 1/16. Add up all the three equations, we get

=> 2(A + B + C)'s one day's work = 1/8 + 1/12 + 1/16 = 26/96.

=> (A + B + C)'s one day's work = 26/192.

=>A's one day's work = (A + B + C)'s one day's work — (B + C)'s one day's

work = 26/192 — 1/12 = (26 — 16)/192 = 10/192.

Since A completes 10/192 of the work in 1 day, he will complete the work in 192/10 = 19.2 days. By a similar logic, B will require 13.7 days and C will require 96 days.

**Question 17:**

A is twice as good a workman as B and together they finish a piece of work in 20 p days. In how many days can A alone finish the work?

[1] 30 days

[2] 25 days

[3] 20 days

[4] 32 days

**Answer:**

**Explanation: **

A's one day's work : B's one day's work = 2 : 1.

=>Out of every three parts of work done, 2 will be done by A and 1 by B

Now, (A B)'s one day's work = 1/20.

A's share = 2/3 x 1/20 = 2/60 = 1/30.

=>In 1 day, A does 1/30 of the work. Hence, A will need a total of 30 days to do the job alone.

**Question 18:**

The rates of working of A and B are in the ratio 4 : 5. What is the ratio of the number of days taken by them to finish a job when working separately?

[1] 2 : 3

[2] 3 : 2

[3] 5 : 4

[4] 4 : 3

**Answer:**

**Explanation: **

The Time Taken is always inversely proportional to the Efficiencies (or the Rates of Working) = time taken by A : B = 5 : 4.

**Question 19:**

Ram can do a piece of work in 20 days which Shyam can do in 30 days. They begin together with the condition that Ram shall leave the job 3 days before the actual completion of work. What is the total number of days required to complete the work?

[1] 14 days

[2] 19 days

[3] 27 days

[4] 9 days

**Answer:**

**Explanation: **

Let X be the days required to complete the work \( \frac{{x - 3}}{{20}} + \frac{x}{{30}} = 1\)

Solving \(x\approx 14\)

**Question 20:**

Rama can do a piece of work in 10 days and Rami alone can do it in 5 days. Rama and Rami undertook to do it for Rs.400. With the help of their neighbour Snooty, they finished it in 2 days. The share of Snooty out of the remuneration is

[1] Rs.120

[2] Rs.200

[3] Rs.160

[4] Rs.180

**Answer:**

**Explanation: **

(Rama + Rami + Snooty)'s one day's work = 1/10 + 1/5 + 1/X.

(Rama + Rami + Snooty)'s two day's work = 2 x (1110 + 1/5 + 1/X).

{because they need 2 days to do the job)

=> 2 [ 1/10 + 115 + 1/X ] = 1 = On solving we get, X = 5 days.

This means that Snooty can do the whole work alone in 5 days.

=> In one day, he does 1/5 of the work.

=>In two days, he does (2 x 1/5) of the work.

=> Snooty's share = 1/5 x 2 x 400 = Rs.160.