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Maths 5 Marks Questions

Time and Work · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 6 questions.

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5 Marks Questions

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6 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 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 25 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 35 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 45 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 55 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 65 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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