Question

A farmer ploughing a certain area of land at the rate of 10m² per hour finished his work at 6
pm. If he ploughs at the rate of 12 m² per hour, he finishes his work at 4p.m. The total square
metre of land he was ploughing was
a. 180 m
b. 120 m
c. 160 m
d. 200 m e. None of these​

Answer 1

Answer:

b) 120 m

Step-by-step explanation:

speed*time= distance (total area here )

10x=12(x-2)

x= 12

total area = 10(12) = 120 m

Answer 2

Answer:

120m²

Step-by-step explanation:

Let the area of the field be A and the total time taken to finish the work at 6pm be x and so the rate of work is 10m²/h

also, let the total time taken to finish the work at 4pm be y and so the rate of work is 12m²/h

We know that as the speed of work increases, time taken to do the work decreases (Think about it......)

so, x > y

we also know that, the time taken for both the cases starts at the same point in time but the difference comes at the end, that is, a 2 hour difference

So, for example if the farmer starts at 12a.m then at a speed of 10m²/h, the work would end at time t and if the speed becomes 12m²/h then it would end at a time (t - 2)

(Similar to the Question where it ends at 6pm and 4pm)

(Think about it.......)

We also know that,

Area of work done = speed × time

A = 10 × x

A = 10x

also,

A = 12 × y

A = 12y

Now the Area of the field is same then

10x = A = 12y

thus, 10x = 12y

we also said that if at 10m²/h time is x then, with a speed of 12m²/h time should be x - 2

so, we get the relation

y = x - 2

Putting this in our equation we get

10x = 12(x - 2)

10x = 12x - 24

12x - 10x = 24

2x = 24

x = 24/2 = 12 hrs

But we need the Area here

so,

A = 10x = 10(12) = 120m²

Hope it helped and you understood it........All the best