## Time and Work

1. A can do a work in 20 days and B in 30 days. In how many days they can complete the work if they work together.

A. 18 days

B. 20 days

C. 21 days

D. 22 days

Explanation:

			A’s one day’s work = $\frac{1}{20}$

B’s one day’s work = $\frac{1}{30}$

(A + B)’s one day work = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{3 + 2}{60}$ = $\frac{5}{60}$ = $\frac{1}{12}$

A and B can complete the work in 12 days			
2. A, B and C complete a work in 6, 8 and 12 days respectively. In how many days they can complete the work together.

A. 18 days

B. 20 days

C. 21 days

D. 22 days

Explanation:

			A’s one day’s work = $\frac{1}{6}$

B’s one day’s work = $\frac{1}{8}$

C’s one day’s work = $\frac{1}{12}$

(A+B+C)’s one day work = $\frac{1}{6}$ + $\frac{1}{8}+\frac{1}{12}$ = $\frac{4+3+2}{24}$ = $\frac{9}{24}$ = $\frac{3}{8}$

(A+B+C) will complete the work = 1$\div$ $\frac{3}{8}$ = $\frac{8}{3}$ = 2$\frac{2}{3}$

\underline{Shortcut Method}

$\frac{6\times 8\times 12}{6\times 8+6\times 12+8\times 12}$ = $\frac{8}{3}$ = 2$\frac{2}{3}$

$\lbrack \frac{t_{1 \times }t_{2 \times }t_{3}}{t_{1} t_{2}+t_{1} t_{3}+t_{2}t_{3}} \rbrack$			
3. A and B together complete a work in 12 days. B alone can complete the work in 28 days. A alone can do the work in how many days.

A. 18 days

B. 20 days

C. 21 days

D. 22 days

Explanation:

			(A+B)’s one day’s work = $\frac{1}{12}$

B’s one day work = $\frac{1}{28}$                                                        $\lbrack (A+B)- (B) = A\rbrack$

A’s one day work = $\frac{1}{12}$ - $\frac{1}{28}$ = $\frac{7-3}{84}$ = $\frac{4}{84}$ = $\frac{1}{21}$

So, A can do it in 21 days


4. A, B complete a work in 25, 20 days respectively. after working together for 5 days A left. B complete the work in

A. 18 days

B. 20 days

C. 21 days

D. 22 days

Explanation:

			(A+B)’s 5 days work = 5$\lbrack \frac{1}{25}+\frac{1}{20}\rbrack$

= 5$\lbrack \frac{4+5}{100}\rbrack$

= 5 $\lbrack \frac{9}{100}\rbrack$

= $\frac{9}{20}$

Remaining work = 1 - $\frac{9}{20}$ = $\frac{11}{20}$

B can complete $\frac{11}{20}$ work = $\frac{11}{20}$ $\times$ 20 = 11s			
5. A, B can dig a well in 10 days and 12 days respectively. If Rs.11 is for total work what is A share.

A. 18 days

B. 20 days

C. 21 days

D. 22 days

			A’ s one day’s work = $\frac{1}{10}$
B’ s one day’s work = $\frac{1}{12}$
Ratio of (A+B)’s one day work = $\frac{1}{10} : \frac{1}{12}$ = 6 : 5
A’s  share = $\frac{6}{11}$ $\times$ 11 = Rs. 6