Today I am going to share techniques to solve Time and Work question. I have already shared a technique for this chapter here.
his topic is based on two main concepts:
- ONE DAY WORK: Unitary Method
- TOTAL WORK
Let us pick up a question to understand it .
Question - A can do a piece of work in 10 days and B can do the same work in 15 days. How long will they take to do the work together.Answer -
A =10 days
B = 15 days
A+B = ? days
To answer we can apply two methods.
According to the first method
If A can do a piece of work in 10 days
A’s one day work = 1/10
Similarly B’s one day work = 1/15
![Time and work Time and work](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYH8W6mzHIw99Od3A_VCVynbnud4aGdZgecvY5mw5mn8AmbuzQKCCG4SjtJtuNsqmOnb9Pg6pcwWzy1pgjsXTAAWVXT9K2OB00Q8d9bvs5P35-F2JlcxNAvWIYaygQBo0nJHUskbvv9D8/s400/1.png)
So this method says that
⇒ To do 1/6 work (A+B) take = 1 day
⇒ To do 1 work (A+B) take = 1/ (1/6) = 1 x6/1 = 6 days
Based on this method , the shortcut would be:
![Time and work 3 Time and work 3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSRhX8j5UhQvZRfbRFFZ2-dbuKbm2NIXqj325StjFdqPPJbWSSPd6JQC4zwzpqZQXR2uUuDMWCT1abx9zJ8U4xPEVC_XL8ZINMfryBNj-nyOSvgoRa1mDH1cprvA888xDWq50YrbxKWsY/s640/3.png)
SECOND METHOD :
A = 10 days
B = 15 days
⇒ Total work = 30 units
WHY 30 units ?
⇒ Remember the LCM of 10 and 15 is 30.
⇒ A does 1 work in 10 days so in one A will do = 30/10 = 3 units
⇒ B does 1 work in 15 days so in 1 day B will do = 30/15 = 2 units
⇒ So together ( A+B) complete = 3+2 = 5 units in one day
![Time and work 5 Time and work 5](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw6e8LGK6E_QPcWz-iZNegLWmSOk2xrSaKWAlQuBAuP8niWv3LJehVAQbH1Y0YJMbOCG0m6srh3fbkNh8X4AmHSnqjPIGRKC-41nbs87UWNg6CvWn9l9NmooC4KPPF9MewZxLPyisRM6w/s400/4.png)
Now which method to be applied, depends upon the kind of
questions asked and your comfort level.
Solution -
![Time and work 6 Time and work 6](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeJI5seb4fJ6a8AkPVQSNWklssj2egemrcj-lMaKMZvjivXUxXg3DogZCKyBl4Ho1D1XIb1xFRiDDF7CVDwyNR6k2N9nRaQWWyT1CW5zNT_32_jU2pfPKxN4sMQQGxUkG9fLwCvJTgrjM/s640/5.png)
![Time and work 7 Time and work 7](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNBo2kQZs4T4c8c3jJ5pcGRAcyrgggd-tXxub_Rn3-fBfh-6eQnFoinWb3PUX1BKx4-LydioMJ18RXrZSA2Qne6-P3V3qHqTFg49_oOqP35RZQA38Qn8JNDVay8oToImIrye1KSjeJcsk/s640/6.png)
![Time and work 8 Time and work 8](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhURv58XvdRp5bcd4vELHvKx6MdOtpuTPeXpS-qEi1sPzVec6Z-Q8nb9m21S0GFvWDsTpBYHZ5DdNc1P0xO_9pBLmCJ-T951t4YJla1Flr_tAAaDkshFb4t5txuwOWUdCJNSsA8kE-zjC8/s400/7.png)
![Time and work 10 Time and work 10](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSgGdk5s9A8zZ-8JBnCZvB4JcHEUP2j8LEAQBiF8K8pnnQyFmfTexeGha9JtzRSx9t2uZrmAxUbfhqtTn1xZRVfNfTeyRfrP0EOViX9I3ouTn-_h2V5sziz3LvJur7Eveo3X9kbcLNSHY/s1600/8.png)
![Time and work 11 Time and work 11](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRqTT4VP8bZq-VkLNz5I3Fac4TWTbFkpnRd_gTkRTZf6qvfWb0u_iJaef0j8NDHrHRZnfHAA29A8sZvV3fyU-weN4A-P0iujhf3znSjf6n62PVuAU_ugrPjiy5yRjQxMRY3O1PZqOQqRE/s640/9.png)
![Time and work 13 Time and work 13](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVfpDnTuzedOw4j9RZ-e4rQS4LfDOVjaG9cSG16imGLVsZg2Yd1CqhJku9Idr-LnQCHaODAGJ9EE5zp2io52gSgVan1C7XPFLfyQGcG5nKSd6ZvYfjfLjwZuTqgnLogvrS8j1we9QA8aA/s640/10.png)
![Time and work 6 Time and work 6](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeJI5seb4fJ6a8AkPVQSNWklssj2egemrcj-lMaKMZvjivXUxXg3DogZCKyBl4Ho1D1XIb1xFRiDDF7CVDwyNR6k2N9nRaQWWyT1CW5zNT_32_jU2pfPKxN4sMQQGxUkG9fLwCvJTgrjM/s640/5.png)
According to the second method
![Time and work 7 Time and work 7](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNBo2kQZs4T4c8c3jJ5pcGRAcyrgggd-tXxub_Rn3-fBfh-6eQnFoinWb3PUX1BKx4-LydioMJ18RXrZSA2Qne6-P3V3qHqTFg49_oOqP35RZQA38Qn8JNDVay8oToImIrye1KSjeJcsk/s640/6.png)
![Time and work 8 Time and work 8](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhURv58XvdRp5bcd4vELHvKx6MdOtpuTPeXpS-qEi1sPzVec6Z-Q8nb9m21S0GFvWDsTpBYHZ5DdNc1P0xO_9pBLmCJ-T951t4YJla1Flr_tAAaDkshFb4t5txuwOWUdCJNSsA8kE-zjC8/s400/7.png)
Now according to the third method:
![Time and work 10 Time and work 10](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSgGdk5s9A8zZ-8JBnCZvB4JcHEUP2j8LEAQBiF8K8pnnQyFmfTexeGha9JtzRSx9t2uZrmAxUbfhqtTn1xZRVfNfTeyRfrP0EOViX9I3ouTn-_h2V5sziz3LvJur7Eveo3X9kbcLNSHY/s1600/8.png)
⇒ Now the LCM of 10 and 6 is 30 .
⇒ Total work = 30 units
⇒ A+B take 6 days to complete 30 units
So in 1 day A+B will complete = 30/6 = 5 units
Similarly A will complete= 30/10 =3 units
⇒ And therefore B will complete = 5-3 = 2 units
Now B completes 2 units in = 1 day
⇒ B completes 1 unit in = 1/2 day
⇒ B completes 30 units = 1/2×30=15 days
The same concept could be applied in different questions of TIME AND WORK.
Question - A can do a work in 10 days . B can do the same work in 20 days . They both started together but after 2 days A left.The remaining work was done alone by B.How long A and B both took to complete the work?![Time and work 11 Time and work 11](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRqTT4VP8bZq-VkLNz5I3Fac4TWTbFkpnRd_gTkRTZf6qvfWb0u_iJaef0j8NDHrHRZnfHAA29A8sZvV3fyU-weN4A-P0iujhf3znSjf6n62PVuAU_ugrPjiy5yRjQxMRY3O1PZqOQqRE/s640/9.png)
Work done by A in one day = 1/10
⇒So the work done by A in 2 days = 2/10
Work done by B in one day = 1/20
Work done by B in 2 days = 2/20
⇒ Again work done by B in x days = x/20
Together they completed 1 work
![Time and work 13 Time and work 13](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVfpDnTuzedOw4j9RZ-e4rQS4LfDOVjaG9cSG16imGLVsZg2Yd1CqhJku9Idr-LnQCHaODAGJ9EE5zp2io52gSgVan1C7XPFLfyQGcG5nKSd6ZvYfjfLjwZuTqgnLogvrS8j1we9QA8aA/s640/10.png)
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