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GATE 2018 ME (ME2) – Question 8

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · MTA

A contract must be completed in 52 days. There are 125 identical robots, each operating 7 hours/day. After 39 days, five-sevenths of the work is complete. How many additional robots are required to finish on time if each now operates 8 hours/day?

  1. 50
  2. 89
  3. 146
  4. 175

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Correct answer: MTA

Explanation

The official key awards **marks to all**. Completed work requires $125(7)(39)=34125$ robot-hours and equals five-sevenths of the total. Remaining work is $34125(2/5)=13650$ robot-hours. Remaining time is 13 days of 8 h/day, requiring $13650/(13\times8)=131.25$ robot equivalents. Thus 132 whole robots, or **7 additional robots**, are needed. None of the choices fits.