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Solved Example #11

Wednesday, January 22nd, 2014

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A team of miner planned to mine 1800 tonnes in a certain number of days.Due to some difficulties in one third of the planned days, the team was able to achieve an output of 20 tons of ore less than the planned output.To make up for this, the team overachieved for the rest of the days by 20 tons.The end result for this that they completed the one day ahead of time.How many tone of ore did the team initially plan to ore per day?

a. 50

b. 100

c.  150

d.  200

e.  250

 

 

Answer : 

Let us assume the no. of days as ‘3d’ and the output per day as ‘x’

Then, 3d*x = 1800 …(1)

 

For the first ‘d’ days, the output was (x-20).

For the next ‘2d-1’ days, the output was (x+20).

 

=> d(x-20) + (2d-1)(x+20) = 1800

=> dx – 20d + 2dx + 40d – x – 20 = 3dx {Replacing 1800 with 3dx from equation (1)}

=> 20d = x + 20

=> d = (x+20)/20 …(2)

 

=> 3 [(x+20)/20] x = 1800

=> x^2 + 20x = (1800/3)*20

=> x^2 + 20x – 12000 = 0

=> (x+120)(x-100) = 0

=> x = -120 or 100

 

Since x is the output it cannot be negative.

So, the initial planned output is 100 tonnes.Thus Option B

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