RS Aggarwal Solutions for Class 8 Maths Chapter 13 Exercise 13.1 (Ex 13A) Time and Work

(Question 3) A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?

Solution:

Solution:

We know that, Number of hours raju requires to do the job $=15$ hours $(x+15/15x)=1/6$ [As they both can finish the job in $6$ hours] $6x+90=15x$ $9x=90$ $x=90/9$ $x=10$ $\therefore$ Siraj can do the work in $10$ hours.

(Question 5) A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?

Solution:

We know that, Number of days $A$ requires to do piece of work $=10$ days Number of days $B$ requires to do the piece of work $=12$ days Number of days $C$ requires to do the piece of work $=15$ days $\therefore$ We can calculate, work done by $A$ in $1$ day $=1/10$ Work done by $B$ in $1$ day $=1/12$ Work done by $C$ in $1$ day $=1/15$ Now, work done by $A,B$ and $C$ together in $1$ day $=1/10+1/12+1/15=15/60=1/4$ $\therefore$ They can do work together in $4$ days.

(Question 6) A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?

(Question 7) A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

(Question 8) 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. Find the total time taken to finish the work.

Solution:

We know that, Number of days $A$ required to do piece of work $=16$ days Number of days $B$ required to do piece of work $=12$ days $\therefore$ We can calculate, work done by $A$ in $1$ day $=1/16$ Work done by $B$ in $1$ day $=1/12$ $A$ alone works for $2$ days so, the amount of work completed by $A$ in $2$ days $=2\times 1/16=1/8$ $\therefore$ work left $=1-1/8=7/8$ Work done by $A,B$ together in a one day $=1/16+1/12=7/48$ $\therefore$ they can complete the work together in $48/7$ days But only $7/8^{th}$ of work is to be completed by both $A$ and $B$ $\therefore$ time required to complete $7/8^{th}$ work together by $A$ and $B=7/8\times 48/7=6$ days Time taken to finish the work $=6+2=8$ days ( $2$ is added because $1/8$ work is done by $A$ alone) $\therefore$ Total time taken to complete the work $=8$ days.

(Question 9) A can do a piece of work in 14 days and 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?

Solution:

$A$ can do a piece of work in $14$ days. Therefore $A^{\prime }s$ one days work will be $\frac{1}{14}$ $B$ can do a piece of work in $21$ days. If $A$ and $B$ together work then their one days work will be $\Rightarrow \frac{1}{A}+\frac{1}{B}=\frac{1}{14}+\frac{1}{21}$ $\Rightarrow \frac{1}{A}+\frac{1}{B}=\frac{3+2}{42}$ taking LCM $\Rightarrow \frac{1}{A}+\frac{1}{B}=\frac{5}{42}$ $A$ and $B$ worked for $6$ days Therefore their $6$ days work is $\frac{5}{42}\times 6=\frac{5}{7}$ Amount of work completed is $\frac{5}{7}$ Work to be completed is $1-\frac{5}{7}=\frac{7-5}{7}=\frac{2}{7}$ Therefore $\frac{2}{7}$ work has to be completed by $B$ only. $=\frac{2}{7}\times 21$ $=2\times 3=6days$ Work will be completed in $6$ days

(Question 10) A can do 2/3 of a certain work in 16 days and B can do ¼ of the same work in 3 days. In how many days can both finish the work, working together?

Benefits of RS Aggarwal Solutions for Class 8 Maths Chapter 13 Exercise 13.1

• Comprehensive Understanding : The solutions provide detailed explanations and step-by-step guidance for each problem, helping students grasp the underlying concepts of Time and Work effectively.
• Problem-Solving Skills : By practicing these solutions students can enhance their ability to solve various types of time and work problems, improving their problem-solving skills and confidence.
• Clarity of Concepts : The solutions clarify complex concepts and formulas related to time and work, making it easier for students to understand and apply them in different scenarios.
• Exam Preparation : Regular practice with these solutions helps students become familiar with the types of questions that may appear in exams leading to better preparation and performance.
• Error Correction : The detailed solutions help students identify and correct their mistakes, fostering a better understanding of how to approach and solve similar problems in the future.
• Time Management : Through these solutions students learn to manage their time efficiently while solving problems, which is important for performing well in timed exams.