If the excavation of earth is done manually then it costs Rs. 100 per cum. A machine can excavate at a fixed cost of Rs. 40,000 plus a variable cost Rs. 20 per cum. The quantity of the earth for which the cost of excavation by machine will be equal to the cost of excavation by machine will be equal to the cost by manual excavation is

If the excavation of earth is done manually then it costs Rs. 100 per cum. A machine can excavate at a fixed cost of Rs. 40,000 plus a variable cost Rs. 20 per cum. The quantity of the earth for which the cost of excavation by machine will be equal to the cost of excavation by machine will be equal to the cost by manual excavation is Correct Answer 500 cum

Concepts:

Let the total quantity for excavation is x cum

Cost of excavation of earth if done manually = Rs. 100 per cum

The total cost of excavation of ‘A’ cum earth if done manually, Ch = Rs. 100 × A cum

Cost of excavation by Machine, Cm = Fixed cost + variable cost                             

Cm = 40000 + 20 × A

It is given that cost of excavation by machine will be equal to the cost of manual excavation is

i.e. Ch = Cm

100 × A= 40000 + 20 × A

 On solving, we get A = 500 cum

∴ The total quantity for excavation is 500 cum

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Neha was solving a problem in which subtraction of 673–257 was required. She said, "257 plus 100 will be 357, 457, 557, 657. So, 257 plus 400 is 657". "Now 657 plus 10 is 667, 677, so, 657 plus 20 is 677 and 4 less in 677 is 673. "Therefore, 400 plus 20 minus 4 is 416". Hence 673–257 is 416. Which of the following statements is most appropriate for the strategy of Neha?