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Chapter 4: Problem 493

Bansi does a given amount of work in \(30 \mathrm{sec}\). Jaimeen does the same amount of work .. in \(15 \mathrm{sec}\). The ratio of the output power of Bansi to the Jaimeen is.... (A) \(1: 1\) (B) \(1: 2\) (C) \(2: 1\) (D) \(5: 3\)

Short Answer

Expert verified
The ratio of the output power of Bansi to Jaimeen is \(1:2\). The answer is (B) \(1: 2\).

Step by step solution

01

Given information

We know that Bansi complete a given amount of work in 30 seconds and Jaimeen complete the same amount of work in 15 seconds. For Bansi: \(Time_1 = 30s\) For Jaimeen: \(Time_2 = 15s\)
02

Compute the output power of Bansi and Jaimeen

Using the equation for power, \(Power = \dfrac{Work}{Time}\), we will calculate the output power for both Bansi and Jaimeen. Let's consider the amount of work done is W. For Bansi: \(Power_1 = \dfrac{W}{Time_1}\) For Jaimeen: \(Power_2 = \dfrac{W}{Time_2}\)
03

Calculate the ratio of the output power

Now we will find the ratio of the output power of Bansi to Jaimeen. \(Ratio = \dfrac{Power_1}{Power_2}\) \(Ratio = \dfrac{\dfrac{W}{Time_1}}{\dfrac{W}{Time_2}}\) As the amount of work (W) is the same for both Bansi and Jaimeen, we can cancel W in the equation: \(Ratio = \dfrac{Time_2}{Time_1}\)
04

Substitute Given Values

Substitute the given values of time for Bansi (30 seconds) and Jaimeen (15 seconds) into the ratio formula: \(Ratio = \dfrac{15}{30}\) Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (15): \(Ratio = \dfrac{1}{2}\)
05

Write the ratio in the form \(x: y\)

To convert the ratio into \(x:y\) form, we can simply take the reciprocals of both numbers: Ratio of the output power of Bansi to Jaimeen: \(1:2\) The answer is (B) \(1: 2\).

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