Quantity , 1: Time taken by Manoj and Shubham | vedclass

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Question

(B) Let the time taken by Manoj and Shubham to complete the work together be $x \, 	ext{hrs}$.
According to the problem:
Time taken by Manoj alone

Vedclass · Accepted Answer

Quantity $I < $ Quantity $II$

Vedclass · Answer

(B) Let the time taken by Manoj and Shubham to complete the work together be $x \, 	ext{hrs}$.
According to the problem:
Time taken by Manoj alone = $(x + 4.8) \, 	ext{hrs}$.
Time taken by Shubham alone = $(x + 10.8) \, 	ext{hrs}$.
Using the work-time formula:
$\frac{1}{x} = \frac{1}{x + 4.8} + \frac{1}{x + 10.8}$
For such problems,the shortcut formula is $x = \sqrt{a 	imes b}$,where $a$ and $b$ are the extra times taken by individuals compared to the combined time.
$x = \sqrt{4.8 	imes 10.8}$
$x = \sqrt{\frac{48}{10} 	imes \frac{108}{10}}$
$x = \sqrt{\frac{5184}{100}}$
$x = \frac{72}{10} = 7.2 \, 	ext{hrs}$.
Quantity $1 = 7.2 \, 	ext{hrs}$.
Quantity $2 = 7.4 \, 	ext{hrs}$.
Since $7.2 < 7.4$,Quantity $1 < $ Quantity $2$.

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