Ramesh can complete a work in 20 days. Mohan is 66.67% as efficient as Ramesh. Mohan and Ramesh begin to work together. Ramesh leaves after working for some days. The remaining work is completed by Mohan in 10 days. After how many days does Ramesh leave the work?
Question
Ramesh can complete a work in 20 days. Mohan is 66.67% as efficient as Ramesh. Mohan and Ramesh begin to work together. Ramesh leaves after working for some days. The remaining work is completed by Mohan in 10 days. After how many days does Ramesh leave the work?
Solution 1
Let's solve this step by step:
Step 1: We know that Ramesh can complete the work in 20 days. So, his work rate is 1/20 of the work per day.
Step 2: Mohan is 66.67% as efficient as Ramesh. So, Mohan's work rate is 66.67/100 * 1/20 = 1/30 of the work per day.
Step 3: Let's assume that Ramesh worked for 'x' days before leaving. So, the work done by Ramesh is x/20.
Step 4: After Ramesh left, Mohan completed the remaining work in 10 days. So, the work done by Mohan is x/30 + 10/30.
Step 5: Since the total work is 1 (as it's the whole job), we can set up the equation: x/20 + x/30 + 10/30 = 1.
Step 6: Solving this equation, we get x = 6 days.
So, Ramesh leaves the work after 6 days.
Solution 2
Let's solve this step by step:
Step 1: We know that Ramesh can complete the work in 20 days. So, his work rate is 1/20 of the work per day.
Step 2: Mohan is 66.67% as efficient as Ramesh. So, Mohan's work rate is 66.67/100 * 1/20 = 1/30 of the work per day.
Step 3: Let's assume that Ramesh worked for 'x' days before leaving. So, the work done by Ramesh is x/20.
Step 4: After Ramesh left, Mohan completed the remaining work in 10 days. So, the work done by Mohan is x/30 + 10/30.
Step 5: Since the total work is 1 (as it's the whole job), we can set up the equation: x/20 + (x+10)/30 = 1.
Step 6: Solving this equation, we get x = 10 days.
So, Ramesh leaves the work after 10 days.
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