A contractor has a large project to complete. He employs a team that completes 3/7 of the total work in the first month and 2/5 of the remaining work in the second month. If the work left to be completed is 120 units, what was the total volume of work?

English বাংলা

Answer

350 units

Explanation

Let the total work be x units. Work done in the first month = 3/7x. Remaining work = x - 3/7x = 4/7x. Work done in the second month = 2/5 of 4/7x = 8/35x. Now, remaining work = 4/7x - 8/35x = (20x - 8x)/35 = 12x/35. According to the question, 12x/35 = 120. Therefore, x = (120 * 35) / 12 = 10 * 35 = 350 units.

Key Points

  • > Calculating the remainder after the first step (1 - 3/7 = 4/7) is crucial.
  • > The 'fraction of the remaining' implies multiplication with the remainder.
  • > Equating the final fractional value to the given real value (120) solves for the total.

Additional Information

  • These types of problems are typically solved using the 'Unitary Method' or 'Fractional Analysis'.
  • In competitive exams, converting fractions to percentages can sometimes simplify the calculations.
  • Remember, if 'remaining' is mentioned, the next fraction must be applied to the current balance, not the original total.
FractionPercentage (%)Decimal
1/250%0.5
1/425%0.25
1/520%0.2
3/742.85%0.428
1/812.5%0.125
Mathematics Time and Work Medium

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Medium