MCQ 11 Mark
Tick the correct answer in the following: A can do a piece of work in $25$ days, which $B$ alone can do in $20$ days. A started the work and was joined by $B$ after $10$ days. The work lasted for:
AnswerCorrect option: C. $16\frac{2}{3}\ \text{days}.$
$A's\ 1$ days work $=\frac{1}{25}$
$B's\ 1$ days work $=\frac{1}{20}$
$A$ and $B's$ days work $=\frac{1}{25}+\frac{1}{20}$
$=\frac{4+5}{100}=\frac{9}{100}$
$A's\ 10$ days work $=\frac{1}{25}\times10=\frac{2}{5}$
Remaining work $=1-\frac{2}{5}=\frac{3}{5}$
$\therefore\frac{3}{5}$ work will be finished by $A$ and $B$ in,
$=\frac{3}{5}\times\frac{100}{9}=\frac{20}{3}\ \text{days}=6\frac{2}{3}\ \text{days,}$
$\therefore$ Whole work was finished in $=10+6\frac{2}{3}$
$=16\frac{2}{3}\ \text{days}.$
View full question & answer→MCQ 21 Mark
Tick the correct answer in the following: $3$ men or $5$ women can do a work in $12$ days. How long will $6$ men and $5$ women take to do it?
- A
$6$ days.
- B
$5$ days.
- ✓
$4$ days.
- D
$3$ days.
AnswerCorrect option: C. $4$ days.
$3$ men $= 5$ women
$1$ men $\frac{5}{3}$ women $5$
$6$ men $=\frac{5}{3}\times6=10$ women,
$\therefore$ Total women in second case,
$= 10 + 5 = 15$ women
Now,
$5$ women $: 15$ women $: 12$ days $: x$
$\therefore$ By inverse proportion,
$5 : 15 : x : 12$
$\text{x}=\frac{5\times12}{15}=4\ \text{days}$
View full question & answer→MCQ 31 Mark
Tick the correct answer in the following: $A$ and $B$ together can do a piece of work in $12$ days; $B$ and $C$ can do it in $20$ days while $C$ and $A$ can do it in $15$ days. $A, B$ and $C$ all working together can do it in
- A
$6$ days.
- B
$9$ days.
- ✓
$10$ days.
- D
$10\frac{1}{2}$ days.
AnswerCorrect option: C. $10$ days.
$A$ and $B's\ 1$ day's work $=\frac{1}{12}$
$B$ and $C's\ 1$ day's work $=\frac{1}{20}$
$C$ and $A's\ 1$ day's work $=\frac{1}{15}$
Adding we get,
$2(A, B$ and $C)'s\ 1$ day's work,
$=\frac{1}{12}+\frac{1}{20}+\frac{1}{15}$
$=\frac{5+3+4}{60}=\frac{12}{60}=\frac{1}{5}$
$\therefore A, B$ and $C's\ 1$ days work,
$=\frac{1}{5}\times\frac{1}{2}=\frac{1}{10}$
$\therefore$ That will finish the work in $= 10$ days.
View full question & answer→MCQ 41 Mark
Mark againts the correct answer in the following: The rates of working of two tapes $A$ and $B$ are in the ratio $2 : 3$. The ratio of the time taken by $A$ and $B$ respectively to fill a given cistern is:
- A
$2 : 3$
- ✓
$3 : 2$
- C
$4 : 9$
- D
$9 : 4$
AnswerCorrect option: B. $3 : 2$
Rates at which taps $A$ and $B$ work $= 2 : 3$
The ratio of time taken by taps $A$ and $B$ to fill the cistern,
$=\frac{1}{\text{Rate at which taps A and B work}}$
$=\frac{1}{\frac{2}{3}}=\frac{3}{2}=3:2$
View full question & answer→MCQ 51 Mark
Tick the correct answer in the following:A can do a piece of work in $15$ days. $B$ is $50\%$ more efficient than $A. B$ can finish it in:
AnswerCorrect option: A. $10\ \text{days}.$
$A's\ 1$ day's work $=\frac{1}{15}$
Then $B's$ day's work $=\frac{1}{10}\times\frac{100+50}{100}$
$=\frac{1}{15}\times\frac{150}{100}$
$=\frac{1}{10}$
$B$ will finish the work in $10$ days.
View full question & answer→MCQ 61 Mark
Tick the correct answer in the following: A can do a job in $16$ days and $B$ can do the same job in $12$ days. With the help of $C,$ they can finish the job in $6$ days only. Then, $C$ alone can finish it in
- A
$34$ days.
- B
$22$ days.
- C
$36$ dyas.
- ✓
$48$ days.
AnswerCorrect option: D. $48$ days.
$A's\ 1$ day's work $=\frac{1}{16}$
$B's\ 1$ day's work $=\frac{1}{12}$
$\therefore C's\ 1 $ days work $=\frac{1}{6}-\Big(\frac{1}{16}+\frac{1}{12}\Big)$
$=\frac{1}{6}-\frac{1}{16}-\frac{1}{12}$
$=\frac{8-3-4}{48}=\frac{1}{48}$
$\therefore C$ can finish the work in $= 48$ days.
View full question & answer→MCQ 71 Mark
Tick the correct answer in the following: $A$ can do a piece of work in $20$ days which $B$ alone can do in $12$ days. $B$ worked at it for $9$ days. $A$ can finish the remaining work in:
- A
$3$ days.
- ✓
$5$ days.
- C
$7$ days.
- D
$11$ days.
AnswerCorrect option: B. $5$ days.
$A's\ 1$ day's work $=\frac{1}{20}$
$B's\ 1$ day's work $=\frac{1}{12}$
Both's $1$ day's work $=\frac{1}{20}+\frac{1}{12}$
$=\frac{3+5}{60}=\frac{8}{60}=\frac{2}{15}$
$B's\ 9$ day's work $=\frac{1}{12}\times9\frac{3}{4}$
Remaining work $=1-\frac{3}{4}=\frac{1}{4}$
$\therefore$ A will finish $\frac{1}{4}$ work in $=20\times\frac{4}{1}$
$= 5$ days.
View full question & answer→MCQ 81 Mark
Mark againts the correct answer in the following: $A$ works twice as fast as $B$. If both of them can together finish a peice of work in $12$ hours, then $B$ alone can do it in:
- A
$24$ hours.
- B
$27$ hours.
- ✓
$36$ hours.
- D
$18$ hours.
AnswerCorrect option: C. $36$ hours.
Suppose $B$ takes $x$ hours to complete the work.
$\therefore B's$ $1$ hour work $=\frac{1}{\text{x}}$
A works twice as fast as $B.$
$\therefore A's\ 1$ hour work $=\frac{2}{\text{x}}$
$\frac{1}{12}=\frac{1}{}\text{x}+\frac{2}{\text{x}}=\frac{3 }{\text{x}}$
$\Rightarrow\text{x}=36$ hours.
View full question & answer→MCQ 91 Mark
Tick the correct answer in the following: Two pipes can fill a tank in $10$ hours and $12$ hours respectively, while a third pipe empties the full tank in $20$ hours. If all the three pipes operate simultaneously, in how much time will the tank be full$?$
- A
$7$ hours $15$ minutes.
- B
$7$ hours $30$ minutes.
- C
$7$ hours $45$ minutes.
- ✓
$8$ hours.
AnswerCorrect option: D. $8$ hours.
Frist inlet pipe's $1$ hour work $=\frac{1}{10}$
Second inlet pipe's $1$ hour work $=\frac{1}{12}$
Third outlet pipe's one hour work $=\frac{1}{20}$
$\therefore$ Three outlet pipe's $1$ hour work,
$=\frac{1}{10}+\frac{1}{12}-\frac{1}{20}$
$=\frac{6+5-3}{60}=\frac{8}{60}=\frac{2}{15}$
$\therefore$ The tank will be full in $\frac{15}{2}$ hours $= 7$
$7$ hours $30$ minutes.
View full question & answer→MCQ 101 Mark
Mark againts the correct answer in the following: $A$ can finish a piece of work in $12$ hours while $B$ can finish it in $15$ hours. How long will both take to finish it, working together$?$
- A
$9\text{ hours}.$
- ✓
$6\frac{2}{3}\text{ hours}.$
- C
$6\frac{3}{4}\ \text{hours}.$
- D
$8\frac{1}{3}\ \text{hours}.$
AnswerCorrect option: B. $6\frac{2}{3}\text{ hours}.$
$A's \ 1$ hours work $=\frac{1}{12}$
$B's\ 1$ hours work $=\frac{1}{15}$
$(A + B)'s\ 1$ hours work $=\frac{1}{12}+\frac{1}{15}=\frac{9}{60}=\frac{3}{20}$
Time taken by $A$ and $B$ to complete the work together $=\frac{20}{3}=6\frac{2}{3}$ hours.
View full question & answer→MCQ 111 Mark
Mark againts the correct answer in the following: $A$ can do a piece of work in $14$ days and $B$ is $40\%$ more efficient than A. In how many days can B finish it$?$
- ✓
$10\ \text{days}.$
- B
$7\frac{1}{2}\ \text{days}.$
- C
$5\frac{1}{4}\ \text{days}.$
- D
$5\frac{3}{5}\ \text{days}.$
AnswerCorrect option: A. $10\ \text{days}.$
$A's\ 1$ day work $=\frac{1}{14}$
$B$ is $40\%$ more efficient than $A.$
$\therefore$ $B's\ 1$ day work $=\frac{140}{100}\times\frac{1}{14}=\frac{1}{10}$
$B$ takes $10$ days to complete the work.
View full question & answer→MCQ 121 Mark
Tick the correct answer in the following: The rates of working of $A$ and $B$ are in the ratio $3 : 4.$ The number of days taken by them to finish the work are in the ratio:
- A
$3 : 4$
- B
$9 : 16$
- ✓
$4 : 3$
- D
$16 : 9$
AnswerCorrect option: C. $4 : 3$
Ratio in the rates of working of $A$ and $B = 3 : 4$
Ratio in time = $=\frac{1}{3}:\frac{1}{4}$
$=\frac{4:3}{12}$
$=4:3$
View full question & answer→MCQ 131 Mark
Tick the correct answer in the following: A man can do a piece of work in $5$ days. He and his son working together can finish it in $3$ days. In how many days can the son do it alone$?$
AnswerCorrect option: C. $7\frac{1}{2}\ \text{days}$
A man's $1$ day work $=\frac{1}{5}$
Man and his son's $1$ days work $=\frac{1}{3}$
$\therefore$ Son's $1$ days work $=\frac{1}{3}-\frac{1}{5}$
$=\frac{5-3}{15}=\frac{2}{15}$
$\therefore$ His son will finish the work,
$=\frac{15}{2}\ \text{day}=7\frac{1}{2}\ \text{days}$
View full question & answer→MCQ 141 Mark
Tick the correct answer in the following: A tap can fill a cistern in 8 hours and another tap can empty the full cistern in $16$ hours. If both the taps are open, the time taken to fill the cistern is:
- A
$5\frac{1}{3}$ hours.
- B
$10$ hours.
- ✓
$16$ hours.
- D
$20 $ hours.
AnswerCorrect option: C. $16$ hours.
Frist tap's $1$ hours work to fill $=\frac{1}{8}$
Second tap's $1$ hours work to empty $=\frac{1}{16}$
Both $1$ hour can fill the cistern
$=\frac{1}{8}-\frac{1}{16}=1$
$=\frac{2-1}{16}=\frac{1}{16}$
$\therefore$ The cistern will fill up in $16$ hours.
View full question & answer→MCQ 151 Mark
Tick the correct answer in the following: $A$ pump can fill a tank in $2$ hours. Due to a leak in the tank it takes $2\frac{1}{3}$ hours to fill the tank. The leak can empty the full tank in:
- A
$2\frac{1}{3}$ hours.
- B
$7$ hours.
- C
$8$ hours.
- ✓
$14$ hours.
AnswerCorrect option: D. $14$ hours.
Frist pump's $1$ hours work to fill $=\frac{1}{2}$
Due to leakage, tank is filled in $2\frac{1}{3}$ hours,
$=\frac{7}{3}$ hours,
Both its one hour work $=\frac{3}{7}$
$\therefore$ Leakage's $1$ hour work to empty the tank,
$=\frac{1}{2}-\frac{3}{7}$
$=\frac{7-6}{14}=\frac{1}{14}$
$\therefore$ Leak will empty the tank in $14$ hours.
View full question & answer→MCQ 161 Mark
Tick the correct answer in the following: To complete a work, $A$ takes $50\%$ more time than $B.$ If together they take $18$ days to complete the work, how much time shall $B$ take to do it$?$
- ✓
$30$ days.
- B
$35$ days.
- C
$40$ days.
- D
$45$ days.
AnswerCorrect option: A. $30$ days.
Let $B$ can do a work in $= x$ days,
Then $A$ can do the work,
$=\text{x}+\frac{\text{x}}{2}=\frac{3}{2}\text{x}\ \text{days}$
$A$ and $B\ 1$ days work $=\frac{1}{18}$
$A's\ 1$ days's work $=\frac{1}{\text{x}}$
And $B's\ 1$ days work $=\frac{2}{3\text{x}}$
$\therefore\frac{1}{\text{x}}+\frac{2}{3\text{x}}=\frac{1}{18}$
$\frac{5}{3\text{x}}=\frac{1}{18}\Rightarrow3\text{x}=5\times18$
$\Rightarrow\text{x}=\frac{5\times18}{3}=30$
$\therefore B$ can do the work in $= 30$ days.
View full question & answer→MCQ 171 Mark
Tick the correct answer in the following: $A$ alone can do a piece of work in $10$ days and $B$ alone can do it in $15$ days. In how many days will $A$ and $B$ together do the same work$?$
- A
$5$ days.
- ✓
$6$ days.
- C
$8$ days.
- D
$9$ days.
AnswerCorrect option: B. $6$ days.
$A's\ 1$ day's work $=\frac{1}{10}$
$B's\ 1$ day's work $=\frac{1}{15}$
$\therefore$ Both $A$ and $B's\ 1$ day's work,
$=\frac{1}{10}+\frac{1}{15}$
$=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$
$\therefore A$ and $B$ can do the work in $6$ days.
View full question & answer→MCQ 181 Mark
Tick the correct answer in the following: $A$ works twice as fast as $B.$ If both of them can together finish a piece of work in $12$ days, then $B$ alone can do it in:
- A
$24$ days.
- B
$27$ days.
- ✓
$36$ days.
- D
$48$ days.
AnswerCorrect option: C. $36$ days.
Let $B's\ 1$ day's work $= x$
Then $A's\ 1$ day's work $= 2x$
$A$ and $B's\ 1$ day's work $=\frac{1}{12}$
$\therefore\text{x}+2\text{x}=\frac{1}{12}\Rightarrow3\text{x}=\frac{1}{12}$
$\Rightarrow\text{x}=\frac{1}{12\times3}=\frac{1}{36}$
$\therefore B$ can do the work in $36$ days.
View full question & answer→MCQ 191 Mark
Tick the correct answer in the following: Two pipes can fill a tank in $20$ minutes and $30$ minutes respectively. If both the pipes are opened simultaneously, then hte tank will be filled in:
- A
$10$ minutes.
- ✓
$12$ minutes.
- C
$15$ minutes.
- D
$25$ minutes.
AnswerCorrect option: B. $12$ minutes.
Frist pipe $1$ minutes work $=\frac{1}{20}$
Second pipe $1$ minutes work $=\frac{1}{30}$
$\therefore$ Both's $1$ minutes work $=\frac{1}{20}+\frac{1}{30}$
$=\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$
$\therefore$ Both's $1$ will do the work in $= 12$ minutes.
View full question & answer→MCQ 201 Mark
Tick the correct answer in the following: $A$ does $20\%$ less work than $B.$ If $A$ can finish a piece of work in $7\frac{1}{2}$ hours, then $B$ can finish it in:
AnswerCorrect option: C. $6\ \text{hours}.$
$A's$ hour's work $=\frac{2}{15}$
$A$ and $B's$ ratio in work $=\frac{100-20}{100}:1$
$=\frac{80}{100}:1$
$=\frac{4}{5}:1$
Let ratio be, $\frac{4}{5} x$ and $x,$ then,
$\frac{4}{5}:1=\frac{2}{15}:\frac{1}{\text{x}}$
$1\times\frac{2}{15}=\frac{4}{5}\times\frac{1}{\text{x}}=\frac{2}{15}=\frac{4}{5\text{x}}$
$2\times5\text{x}=4\times15\Rightarrow\text{x}=\frac{4\times15}{2\times5}=6$
$\therefore B$ can finish the work in $6$ hours.
View full question & answer→MCQ 211 Mark
Mark againts the correct answer in the following: A pump can fill a cistern in $2$ hours. Due to a leak in the tank it takes $2\frac{1}{3}$ hours to fill it. The leak can empty the full tank in:
- A
$7$ hours.
- ✓
$14$ hours.
- C
$8$ hours.
- D
$3$ hours.
AnswerCorrect option: B. $14$ hours.
A pump fills a tank in $2$ hours.
Part of tank filled by the pump in one hour $=\frac{1}{2}$
Let $x$ hours be the time required for water to leak from the cistern.
Part of tank drained by the leak in one hour $=-\frac{1}{\text{x}}$
ime required to fill the leaking cistern $=2\frac{1}{3}=\frac{7}{3}$ hours.
Part of tank stored with water in one hour $=\frac{3}{7}$
$\Rightarrow\frac{3}{7}=\frac{1}{2}-\frac{1}{\text{x}}$
$\frac{1}{\text{x}}=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14}$
$\text{x}=14$ hours.
View full question & answer→MCQ 221 Mark
Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be full?
MCQ 231 Mark
A pump can fill a tank in 2 hours. Due to a leak in the tank it takes $2 \frac{1}{3}$ hours to fill the tank. The leak can empty the full tank in
Hint. Work done by the leak in 1 hour $=\left(\frac{1}{2}-\frac{3}{7}\right)=\frac{1}{14}$.
- A
$2 \frac{1}{3}$ hours
- B
- C
- ✓
View full question & answer→MCQ 241 Mark
A tap can fill a cistern in 8 hours and another tap can empty the full cistern in 16 hours. If both the taps are open, the time taken to fill the cistern is
- A
$5 \frac{1}{3}$ hours
- B
- ✓
- D
View full question & answer→MCQ 251 Mark
Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in
MCQ 261 Mark
A can do a piece of work in 25 days, which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for
- A
$12 \frac{1}{2}$ days
- B
- ✓
$16 \frac{2}{3}$ days
- D
AnswerCorrect option: C. $16 \frac{2}{3}$ days
View full question & answer→MCQ 271 Mark
A can do a piece of work in 20 days which B alone can do in 12 days. B worked at it for 9 days. A can finish the remaining work in
MCQ 281 Mark
A does $20 \%$ less work than B. If A can finish a piece of work in $7 \frac{1}{2}$ hours, then B can finish it in
Hint. Ratio of work done by $A$ and $B=$ inverse ratio of time taken by $A$ and $B$.
$\frac{4}{5}: 1=\frac{2}{15}: \frac{1}{x} \Rightarrow x=6 hrs$.
- A
- B
$5 \frac{1}{2}$ hours
- ✓
- D
$6 \frac{1}{2}$ hours
View full question & answer→MCQ 291 Mark
A can do a piece of work in 15 days. B is $50 \%$ more efficient than A. B can finish it in
Hint. A's 1 day's work $=\frac{1}{15}$, B's 1 day's work $=150 \%$ of $\frac{1}{15}=\frac{150}{100} \times \frac{1}{15}=\frac{1}{10}$.
- ✓
- B
$7 \frac{1}{2}$ days
- C
- D
$10 \frac{1}{2}$ days
View full question & answer→MCQ 301 Mark
3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?
MCQ 311 Mark
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
- A
- B
- ✓
- D
$10 \frac{1}{2}$ days
View full question & answer→MCQ 321 Mark
The rates of working of $A$ and $B$ are in the ratio $3: 4$. The number of days taken by them to finish the work are in the ratio
Hint. Ratio of times taken by $A$ and $B=\frac{1}{3}: \frac{1}{4}=4: 3$.
- A
$3: 4$
- B
$9: 16$
- ✓
$4: 3$
- D
$16: 9$
AnswerCorrect option: C. $4: 3$
View full question & answer→MCQ 331 Mark
A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of ₹ 3000, A will get
Hint. Ratio of the wages of $A$ and $B=\frac{1}{10}: \frac{1}{15}=3: 2$.
View full question & answer→MCQ 341 Mark
A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
Hint. Let B's 1 day's work $=x$. Then, A's 1 day's work $=2 x$.
$\therefore x+2 x=\frac{1}{12} \Rightarrow 3 x=\frac{1}{12} \Rightarrow x=\frac{1}{36}$
View full question & answer→MCQ 351 Mark
To complete a work, A takes $50 \%$ more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
Hint. Suppose B takes $x$ days. Then. A takes $\frac{150 x}{100}=\frac{3 x}{2}$ days.
$\therefore \quad \frac{1}{x}+\frac{2}{3 x}=\frac{1}{18} \Rightarrow \frac{5}{3 x}=\frac{1}{18} \Rightarrow x=30$
View full question & answer→MCQ 361 Mark
A can do a job in 16 days and $B$ can do the same job in 12 days. With the help of $C$, they can finish the job in 6 days only. Then, $C$ alone can finish it in
View full question & answer→MCQ 371 Mark
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
- A
$6 \frac{1}{2}$ days
- B
- ✓
$7 \frac{1}{2}$ days
- D
AnswerCorrect option: C. $7 \frac{1}{2}$ days
View full question & answer→MCQ 381 Mark
A alone can do a plece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?