Question

Raju wanted to plough his field. He asked the farmers "how many days will it take to plough the field? The farmers said “The field can be ploughed in 14 days. If 20 hectares of land is ploughed more daily, the work will be finished in 10 days”. Find the area of the land which can be ploughed daily. Also find the area of the field?

Answer 1

1. Area of the land which can be ploughed daily is 50 hectares (and 70 hectares at higher rate)

2. Area of the field is 700 hectares

Explanation:

Let x hectares be the number of hectares the farmers normally ploughed in a day. At this rate, they will complete the work in 14 days, so they have to plough

`14\cdot x=14x\ hectares.`

Then x+20 hectares is the number of hectares the farmers ploughed in a day when they increased their productivity of work. At this rate, they will complete the work in 10 days, so they have to plough

`10\cdot (x+20)=10(x+20)\ hectares.`

The work is the same, so

`14x=10(x+20)\\ \\14x=10x+200\\ \\14x-10x=200\\ \\4x=200\\ \\x=50`

Ploughing 50 hectares each day 14 days in a row they will plough

`14\cdot 50=700\ hectares`