4 Mark Question

Question 14 Marks

A can do a piece of work in 14 days while B can do it in 21 days.They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?

Answer

A's 1 days work $=\frac{1}{14}$
B's 1 days work $=\frac{1}{21}$
A and B's days work $=\frac{1}{14}+\frac{1}{21}$
$=\frac{3+2}{42}=\frac{5}{42}$
A and B's days work $=\frac{5}{42}\times6=\frac{5}{7}$
Remaining work $=1-\frac{5}{7}=\frac{2}{7}$
B will finish $\frac{2}{7}$ work in,
$=\frac{2}{7}\times21=6$ days,
The whole work will finish in = 6 + 6 = 12 days.

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Question 24 Marks

A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Finish the total time taken to finish the work.

Answer

A's one days work $=\frac{1}{16}$
B's one days work $=\frac{1}{12}$
A and B's one day's work $=\frac{1}{16}+\frac{1}{12}$
$=\frac{3+4}{48}=\frac{7}{48}$
A's 2 days work $=\frac{1}{16}\times2=\frac{1}{8}$
Remaining work $=1-\frac{1}{8}=\frac{7}{8}$
A and B will finish the $\frac{7}{8}$ work in,
$=\frac{7}{8}\times\frac{48}{7}=6$ days,
$\therefore$ Whole work will be finished in 2 + 6 = 8 days.

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Question 34 Marks

A and B can do a piece of work in 18 days B days B and C can do it in 24 days while C and A can finish it in 36 days. In many days can A, B and C finish it, if they all work together?

Answer

A and B's one days work $=\frac{1}{18}$
B and C's one days work $=\frac{1}{24}$
C and A's one days work $=\frac{1}{36}$
Adding we get,
2(A + B + C)'s one days work $=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}$
$=\frac{4+3+2}{72}=\frac{9}{72}=\frac{1}{8}$
$\{\text{LCM}\ \text{of}\ 18, 24\ \text{and}\ 36= 72\}$
A, B and C's one days work $\frac{1}{2\times2}=\frac{1}{16}$
A, B and C can do the work in 16 days.

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Question 44 Marks

A can do $\frac{2}{3}$ of a certain work in 16 days and B can do $\frac{1}{4}$ of the same work in 3 days. In how many days can both finish the work, working together?

Answer

A can do $\frac{2}{3}$ work in = 16 days,
A's 1 days work $=\frac{2}{3}\times\frac{1}{16}=\frac{1}{24}$
And B can do $\frac{1}{4}$ of work in = 3 days,
$\therefore$ B's 1 days work $=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$
A and B's both 1 dyas work,
$=\frac{1}{24}+\frac{1}{12}$
$=\frac{1+2}{24}=\frac{3}{24}=\frac{1}{8}$
$\therefore$ Both A and B can do the work in, = 8 days.

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Question 54 Marks

A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. How much time will A alone take to finish the job?

Answer

A and B's one work $=\frac{1}{12}$
B and C's one day's work $=\frac{1}{15}$
C and A's one day's work $=\frac{1}{20}$
$\therefore$ Adding, we get,
2(A + B + C)'s one days work,
$=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}$
$=\frac{5+4+3}{60}(\text{LCM}\ \text{of}\ 12, 15\ \text{and}\ 20= 60)$
$=\frac{12}{60}=\frac{1}{5}$
$\therefore\text{A}+\text{B}+\text{C's}$ one day's work $=\frac{1}{5\times2}=\frac{1}{10}$
A's one day's work $=\frac{1}{10}-\frac{1}{15}$
$=\frac{3-2}{30}=\frac{1}{30}$
$\therefore$ A can do the work in = 30 days.

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Question 64 Marks

A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by A and B?

Answer

A's one days work $=\frac{1}{15}$
b's one days work $=\frac{1}{12}$
C's one day's work $=\frac{1}{20}$
A, B and C's one day's work,
$=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}$
$=\frac{4+5+3}{60}(\text{LCM}\ \text{of}\ 15,12, 20= 60)$
$=\frac{12}{60}=\frac{1}{5}$
A, B and C's 2 days work $=\frac{1}{5}\times2=\frac{2}{5}$
Remaining work $=1-\frac{2}{5}$
$=\frac{5-2}{5}=\frac{3}{5}$
A and B will do the remaining work $\frac{3}{5}$
In $=\frac{20}{3}\times\frac{3}{5}=4$ days.

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