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Question

Assume 'A' does 500 J of work in 'x' minutes and 'B' does 1000 J of work in 20 minutes. If the power delivered by 'A' is \(P_1\) and 'B' is \(P_2\) and \(P_1 = 2P_2\), then 'x', in minutes is:

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is
5

To find the value of \(x\), let's first understand the formula for power. Power (\(P\)) is defined as the work done (\(W\)) over time (\(t\)):

P = \(\frac{W}{t}\)

According to the problem, person 'A' completes 500 J of work in \(x\) minutes, and person 'B' does 1000 J of work in 20 minutes.

Given that the power delivered by 'A', \(P_1\), is twice the power delivered by 'B', \(P_2\):

\(P_1 = 2P_2\)

Now calculate the power delivered by each:

  • For 'A':
  • For 'B':

Simplifying \(P_2\):

\(P_2 = \frac{1000}{1200} = \frac{5}{6} \, \text{W}\)

Substitute the expression for \(P_2\) into the equation \(P_1 = 2P_2\):

\(\frac{500}{x \times 60} = 2 \times \frac{5}{6}\)

Solving the equation:

\(\frac{500}{x \times 60} = \frac{10}{6}\)

Cross-multiply to solve for \(x\):

\(500 \times 6 = 10 \times x \times 60\)

3000 = 600x

\(x = \frac{3000}{600} = 5\)

Therefore, the value of \(x\) is 5 minutes.

Hence, the correct answer is: 5

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