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I want to dig a well so I hire a team of labours according to a plan dig in a depth of 270 metre below the ground level. For the first 3 days labour worked as per plan. However, Subsequently finding that their resources were getting underutilised according to the plan, it started to dig 8 metres more than the plan everyday Therefore, a day before the planned that they had dig to a depth of 280 metres, how many metres of dig was planned every day.

I want to dig a well so I hire a team of labours according to a plan dig in a depth of 270 metre below the ground level. For the first 3 days labour worked as per plan. However, Subsequently finding that their resources were getting underutilised according to the plan, it started to dig 8 metres more than the plan everyday Therefore, a day before the planned that they had dig to a depth of 280 metres, how many metres of dig was planned every day. Correct Answer 30

Given:

According to plan dig in a depth = 270 metres

. For the first 3 days labour worked as per plan

 a day before the planned that they had dig to a depth = 280 metres

Calculations:

Let every day work done by labour x metres and number of days work will done = y days

⇒ x × y = 270      -----(i)

Work done in 3 days = 3x

Everyday work (New) = x + 8

Rest number of days = y – 4

According to question

⇒ 3x + (x + 8) (y -4) = 280

⇒ 3x + xy – 4x + 8y – 32 = 280

Put the value of xy from equation i

⇒ 8y – x = 42      ----- (ii)

From equation i

Put y = 270/x

⇒ x2 + 42x – 2160 = 0

⇒ x2 + 72x – 30x -2160 = 0

⇒ x (x + 72) –30(x + 72) = (x-30) (x + 72)

⇒ x = 30

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