Home
Class 14
MATHS
Vaibhav can do a piece of work in 60 day...

Vaibhav can do a piece of work in 60 days. He works there for 15 days and then Sandeep alone finishes the remaining work in 30 days. In how many days will Vaibhav and Sandeep working together finish the work?

A

20 days

B

24 days

C

18 days

D

22 days

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we need to determine how long it will take for Vaibhav and Sandeep to complete the work together. ### Step 1: Determine Vaibhav's Work Rate Vaibhav can complete the work in 60 days. Therefore, his work rate is: \[ \text{Vaibhav's work rate} = \frac{1}{60} \text{ (work per day)} \] ### Step 2: Calculate Work Done by Vaibhav in 15 Days In 15 days, the amount of work Vaibhav completes is: \[ \text{Work done by Vaibhav in 15 days} = 15 \times \frac{1}{60} = \frac{15}{60} = \frac{1}{4} \] ### Step 3: Determine Remaining Work The total work is considered as 1 unit. After Vaibhav has completed \(\frac{1}{4}\) of the work, the remaining work is: \[ \text{Remaining work} = 1 - \frac{1}{4} = \frac{3}{4} \] ### Step 4: Determine Sandeep's Work Rate Sandeep finishes the remaining \(\frac{3}{4}\) of the work in 30 days. Therefore, his work rate is: \[ \text{Sandeep's work rate} = \frac{\frac{3}{4}}{30} = \frac{3}{120} = \frac{1}{40} \text{ (work per day)} \] ### Step 5: Combined Work Rate of Vaibhav and Sandeep When Vaibhav and Sandeep work together, their combined work rate is: \[ \text{Combined work rate} = \text{Vaibhav's work rate} + \text{Sandeep's work rate} = \frac{1}{60} + \frac{1}{40} \] To add these fractions, we need a common denominator. The least common multiple of 60 and 40 is 120. Thus: \[ \frac{1}{60} = \frac{2}{120}, \quad \frac{1}{40} = \frac{3}{120} \] \[ \text{Combined work rate} = \frac{2}{120} + \frac{3}{120} = \frac{5}{120} = \frac{1}{24} \text{ (work per day)} \] ### Step 6: Calculate Time Taken to Complete the Work Together To find out how many days it will take for Vaibhav and Sandeep to complete the entire work together, we take the reciprocal of their combined work rate: \[ \text{Time taken} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{24}} = 24 \text{ days} \] ### Final Answer Vaibhav and Sandeep working together will finish the work in **24 days**. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

A can do a piece of work in 80 days.He works at it for 10 days and then B alore finishes the remaining work in 42 days.How long will B take to do the entire work alone?

A can do a piece of work in 20 days and B can do the same piece of work in 30 days. They start working together and work for 5 days and then both leave he work. C alone finishes the remaining work in 14 days. In how many days will C alone finish the whole work?

P can do a piece of work in 20 days and Q can do the same piece of work in 60 days. They start working together and work for 5 days and then both leave the work. R alone finishes the remaining work in 10 days. In how many days will R alone finish the whole work?

A can do a piece of work in 34 days. He worked for 14 days and then left. B completed the remaining work in 30 days. In how many days can B alone complete the work?

X and Y can do a piece of work in 30 days. They work together for 6 days and thenX quits and Y finishes the work in 32 days . In how many days can Y do the piece of work alone ?