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. 10 days

B. 11 days

C. 12 days

D. 15 days

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. 10 days

B. 11 days

C. 12 days

D. 15 days

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. 10 days

B. 11 days

C. 12 days

D. 15 days

(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. 10 days

B. 11 days

C. 12 days

D. 15 days

(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. 10 days

B. 11 days

C. 12 days

D. 15 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 Amount should be shared in 6 : 5 ratio A’s share = $\frac{6}{11}$ $\times $ 11 = Rs. 6