Home
Class 14
MATHS
A can cultivate 2/5 the of a land in 6 d...

A can cultivate `2/5` the of a land in 6 days and B can cultivate `1/3` rd of the same land in 10 days. Working together A and B can cultivate `4/5`the of the land in

A

4 days

B

5 days

C

8 days

D

10 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 A and B to cultivate \( \frac{4}{5} \) of the land when working together. ### Step 1: Calculate the daily work rate of A A can cultivate \( \frac{2}{5} \) of the land in 6 days. Therefore, the amount of land A cultivates in one day is calculated as follows: \[ \text{Work done by A in one day} = \frac{2/5}{6} = \frac{2}{5} \times \frac{1}{6} = \frac{2}{30} = \frac{1}{15} \] ### Step 2: Calculate the daily work rate of B B can cultivate \( \frac{1}{3} \) of the land in 10 days. Therefore, the amount of land B cultivates in one day is calculated as follows: \[ \text{Work done by B in one day} = \frac{1/3}{10} = \frac{1}{3} \times \frac{1}{10} = \frac{1}{30} \] ### Step 3: Calculate the combined daily work rate of A and B Now, we add the daily work rates of A and B to find out how much they can cultivate together in one day: \[ \text{Combined work rate} = \text{Work done by A in one day} + \text{Work done by B in one day} \] \[ = \frac{1}{15} + \frac{1}{30} \] To add these fractions, we need a common denominator. The least common multiple of 15 and 30 is 30: \[ \frac{1}{15} = \frac{2}{30} \] \[ \text{Combined work rate} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10} \] ### Step 4: Calculate the time taken to cultivate \( \frac{4}{5} \) of the land Now that we know A and B together can cultivate \( \frac{1}{10} \) of the land in one day, we need to find out how many days it will take to cultivate \( \frac{4}{5} \) of the land: \[ \text{Time taken} = \frac{\text{Amount of land to be cultivated}}{\text{Combined work rate}} = \frac{4/5}{1/10} \] To divide the fractions, we multiply by the reciprocal: \[ = \frac{4}{5} \times 10 = \frac{40}{5} = 8 \] ### Final Answer Thus, A and B together can cultivate \( \frac{4}{5} \) of the land in **8 days**. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

A can do a job in 12 days and B can do the same job in 6 days, in how many days working together they can complete the job?

A can finish 3/5 of a task in 6 days and B can finish 2/3 of the same task in 12 days. A and B worked together for 5 days. C alone completed the remaining task in 8 days. If B and C working together will complete the same task in:

A can finish (2)/(5) of a task in 12 days and B can finish (2)/(3) of the same task in 30 days .They work together for 10 days .C alone completes the remaining task remaining task in 16 days .B and C together will complete (4)/(5) of the same task in :

A can finish (2)/(5) of a task in 12 days and B can finish (2)/(3) of the same task in 30 days. They work together for 10 days. C alone completes the remaining task in 16 days. B and C together will complete (4)/(5) of the same task in:

A can do (2)/(5) of a work in 6 days and B can do (2)/(3) of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:

A can point 6 walls in 5 days. B can point 8 walls (of the same area) in 4 days. Working together, in hown many days can they point 48 walls (of the same area)?

A can do 4/5 of a work in 20 days and B can do 3/4 of the same work in 15 days. They work together for 10 days. C alone completes the remaining work in 1 day. B and C together can complete 3/4 of the same work in: