Questions and Answers Type: | MCQ (Multiple Choice Questions). |

Main Topic: | Quantitative Aptitude. |

Quantitative Aptitude Sub-topic: | Time and Work Aptitude Questions and Answers. |

Number of Questions: | 10 Questions with Solutions. |

- P is twice as efficient as Q, and finish the task \(5\) days earlier than Q. Find number of days required to finish the task by P?
- \(3 \ days\)
- \(4 \ days\)
- \(5 \ days\)
- \(6 \ days\)

Answer: (c) \(5 \ days\)

Solution: Let P can complete the task in \(x\) days and

Q can complete the task in \(2x\) days, then $$ 2x - x = 5 $$ $$ x = 5 $$ Hence, P can finish the task in \(5\) days.

Solution: Let P can complete the task in \(x\) days and

Q can complete the task in \(2x\) days, then $$ 2x - x = 5 $$ $$ x = 5 $$ Hence, P can finish the task in \(5\) days.

- A is four times as efficient as B, and finish the task \(21\) days earlier than B. Find number of days required to finish the task, if both are working simultaneously?
- \(3.5 \ days\)
- \(4.3 \ days\)
- \(5.6 \ days\)
- \(6.1 \ days\)

Answer: (c) \(5.6 \ days\)

Solution: Let A can complete the task in \(x\) days and

B can complete the task in \(4x\) days, then $$ 4x - x = 21 $$ $$ 3x = 21 $$ $$ x = 7 $$ $$ 4x = 28 $$ together they can finish the part of the task $$ = \frac{1}{7} + \frac{1}{28} $$ $$ = \frac{5}{28} $$ Hence, they can finish the task in \(\frac{28}{5}\) days or \(5.6\) days.

Solution: Let A can complete the task in \(x\) days and

B can complete the task in \(4x\) days, then $$ 4x - x = 21 $$ $$ 3x = 21 $$ $$ x = 7 $$ $$ 4x = 28 $$ together they can finish the part of the task $$ = \frac{1}{7} + \frac{1}{28} $$ $$ = \frac{5}{28} $$ Hence, they can finish the task in \(\frac{28}{5}\) days or \(5.6\) days.

- M is five times as efficient as N, and finish the task \(16\) days earlier than N. Find number of days required to finish the task by N?
- \(10 \ days\)
- \(12 \ days\)
- \(15 \ days\)
- \(20 \ days\)

Answer: (d) \(20 \ days\)

Solution: Let M can complete the task in \(x\) days and

N can complete the task in \(5x\) days, then $$ 5x - x = 16 $$ $$ 4x = 16 $$ $$ x = 4 $$ Hence, N can finish the task in \(5x\) = \(20\) days.

Solution: Let M can complete the task in \(x\) days and

N can complete the task in \(5x\) days, then $$ 5x - x = 16 $$ $$ 4x = 16 $$ $$ x = 4 $$ Hence, N can finish the task in \(5x\) = \(20\) days.

- A is twice as efficient as B and together they can finish a task in \(12\) days. Find number of days required to finish the same task by B?
- \(23 \ days\)
- \(28 \ days\)
- \(36 \ days\)
- \(38 \ days\)

Answer: (c) \(36 \ days\)

Solution: Let A can complete the task in \(x\) days and

B can complete the task in \(2x\) days, then $$ \frac{1}{x} + \frac{1}{2x} = \frac{1}{12} $$ $$ x = 18 $$ $$ 2x = 36 $$ Hence, B can finish the task in \(36\) days.

Solution: Let A can complete the task in \(x\) days and

B can complete the task in \(2x\) days, then $$ \frac{1}{x} + \frac{1}{2x} = \frac{1}{12} $$ $$ x = 18 $$ $$ 2x = 36 $$ Hence, B can finish the task in \(36\) days.

- P and Q together can finish a task in \(15\) days and P alone can finish the same task in \(20\) days. Find how many days are required for Q to finish the work alone?
- \(30 \ days\)
- \(40 \ days\)
- \(50 \ days\)
- \(60 \ days\)

Answer: (d) \(60 \ days\)

Solution: part of task Q can finish in one day $$ = \frac{1}{15} - \frac{1}{20} $$ $$ = \frac{1}{60} $$ Hence, Q alone can finish the task in \(60\) days.

Solution: part of task Q can finish in one day $$ = \frac{1}{15} - \frac{1}{20} $$ $$ = \frac{1}{60} $$ Hence, Q alone can finish the task in \(60\) days.

- Vishal is three times as efficient as Rohan, and finish the task \(36\) days earlier than Rohan. Find number of days required to finish the task, if both are working simultaneously?
- \(13.5 \ days\)
- \(14.3 \ days\)
- \(15.6 \ days\)
- \(16.1 \ days\)

Answer: (a) \(13.5 \ days\)

Solution: Let Vishal can complete the task in \(x\) days and

Rohan can complete the task in \(3x\) days, then $$ 3x - x = 36 $$ $$ 2x = 36 $$ $$ x = 18 $$ $$ 3x = 54 $$ together they can finish the part of the task $$ = \frac{1}{18} + \frac{1}{54} $$ $$ = \frac{2}{27} $$ Hence, they can finish the task in \(\frac{27}{2}\) days or \(13.5\) days.

Solution: Let Vishal can complete the task in \(x\) days and

Rohan can complete the task in \(3x\) days, then $$ 3x - x = 36 $$ $$ 2x = 36 $$ $$ x = 18 $$ $$ 3x = 54 $$ together they can finish the part of the task $$ = \frac{1}{18} + \frac{1}{54} $$ $$ = \frac{2}{27} $$ Hence, they can finish the task in \(\frac{27}{2}\) days or \(13.5\) days.

- A can finish a work in \(7\) days and B can finish the same work in \(10\) days, then find how many days are required to finish the work, if both are working together?
- \(3.3 \ days\)
- \(4.1 \ days\)
- \(5.5 \ days\)
- \(6.6 \ days\)

Answer: (b) \(4.1 \ days\)

Solution: Given, \(x = 7 \ days\), \(y = 10 \ days\)

If both A and B start working together then $$ = \frac{xy}{x + y} $$ $$ = \frac{7 \times 10}{7 + 10} $$ $$ = \frac{70}{17} $$ $$ = 4.1 \ days $$ Hence, together they can finish the work in \(4.1 \ days\).

Solution: Given, \(x = 7 \ days\), \(y = 10 \ days\)

If both A and B start working together then $$ = \frac{xy}{x + y} $$ $$ = \frac{7 \times 10}{7 + 10} $$ $$ = \frac{70}{17} $$ $$ = 4.1 \ days $$ Hence, together they can finish the work in \(4.1 \ days\).

- P, Q and R can complete a work in \(10\), \(20\) and \(25\) days respectively. Find in how many days they can together finish the work together?
- \(3.2 \ days\)
- \(4.5 \ days\)
- \(5.2 \ days\)
- \(6.4 \ days\)

Answer: (c) \(5.2 \ days\)

Solution: All three together can finish the work in one day $$ = \frac{1}{10} + \frac{1}{20} + \frac{1}{25} $$ $$ = \frac{19}{100} $$ Hence, together they can finish the work in \(\frac{100}{19}\) days or \(5.2\) days.

Solution: All three together can finish the work in one day $$ = \frac{1}{10} + \frac{1}{20} + \frac{1}{25} $$ $$ = \frac{19}{100} $$ Hence, together they can finish the work in \(\frac{100}{19}\) days or \(5.2\) days.

- A can complete a work in \(4\) days and B can complete the same work in \(6\) days, while C can completely destroy the work in \(12\) days. If they start working at the same time, then in how many days will the work be completed?
- \(3 \ days\)
- \(4 \ days\)
- \(5 \ days\)
- \(6 \ days\)

Answer: (a) \(3 \ days\)

Solution: The part of work completed by A, B and C in one day $$ = \frac{1}{4} + \frac{1}{6} - \frac{1}{12} $$ $$ = \frac{1}{3} $$ Hence, the work will be completed in \(3\) days.

Solution: The part of work completed by A, B and C in one day $$ = \frac{1}{4} + \frac{1}{6} - \frac{1}{12} $$ $$ = \frac{1}{3} $$ Hence, the work will be completed in \(3\) days.

- P and Q can finish a work in \(10\) days, Q and R can finish the same work in \(20\) days and R & P can finish the same work in \(25\) days. If they start working together, then in how many days they will finish the work?
- \(10.5 \ days\)
- \(15.4 \ days\)
- \(17.5 \ days\)
- \(18.3 \ days\)

Answer: (a) \(10.5 \ days\)

Solution: Given, \(x = 10\), \(y = 20\) and \(z = 25\) then $$ = \frac{2xyz}{xy + yz + zx} $$ $$ = \frac{2 \times 10 \times 20 \times 25}{200 + 500 + 250} $$ $$ = \frac{10000}{950} $$ $$ = 10.5 \ days $$

Solution: Given, \(x = 10\), \(y = 20\) and \(z = 25\) then $$ = \frac{2xyz}{xy + yz + zx} $$ $$ = \frac{2 \times 10 \times 20 \times 25}{200 + 500 + 250} $$ $$ = \frac{10000}{950} $$ $$ = 10.5 \ days $$

Lec 1: Time and Work Case (1) and Case (2)
Exercise-1
Lec 2: Time and Work Case (3) and Case (4)
Exercise-2
Lec 3: Concept of Positive and Negative work
Exercise-3
Lec 4: Concept of Pipes and Cisterns
Exercise-4
Lec 5: Concept of Efficiency
Exercise-5