Question

65 A
Section 1 - B
1) If P and Q together can complete a job in 3 days while P
alone can do the same in 12 days, then how many days
would be required by Q to do the job alone?
A) 3 days
B) 4 days
C) 6 days
D) 12 days​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If P and Q together can complete a job in 3 days while P alone can do the same in 12 days, then how many days would be required by Q to do the job alone?

A) 3 days

B) 4 days

C) 6 days

D) 12 days

EVALUATION

Let P & Q can complete the job in x days and y days respectively

Then by the given condition

$\displaystyle \sf{ \frac{3}{x} + \frac{3}{y} = 1 \: \: \: }$

$\displaystyle \sf{ \frac{1}{x} + \frac{1}{y} = \frac{1}{3} \: \: \: - - - - (1) }$

Also

$\displaystyle \sf{ \frac{12}{x} = 1 }$

$\displaystyle \sf{ \frac{1}{x} = \frac{1}{12} \: \: \: - - - - (2) }$

Equation 1 - Equation 2 gives

$\displaystyle \sf{ \frac{1}{y} = \frac{1}{3} - \frac{1}{12} }$

$\displaystyle \sf{ \implies \: \frac{1}{y} = \frac{4 - 1}{12} }$

$\displaystyle \sf{ \implies \: \frac{1}{y} = \frac{3}{12} }$

$\displaystyle \sf{ \implies \: \frac{1}{y} = \frac{1}{4} }$

$\displaystyle \sf{ \implies \: y = 4 }$

Hence the number of days required by Q to do the job alone = 4 days

FINAL ANSWER

Hence the correct option is B) 4 days

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Answer 2

Given : P and Q together can complete a job in 3 days while

P alone can do the same in 12 days,

To find : how many days would be required by Q to do the job alone  

A) 3 days

B) 4 days

C) 6 days

D) 12 days​

Solution:

P alone can do the same in 12 days,

=> P 1 day work  = 1/12

P alone can do the same in Q days,

=> Q 1 day work  = 1/Q

P and Q together can complete a job in 3 days

=>  P and Q 1 day work  = 1/3

1/12 + 1/Q  = 1/3

=> 1/Q  = 1/3 - 1/12

=> 1/Q = ( 4 - 1) / 12

=> 1/Q  = 3/12

=> 1/Q = 1/4

=> Q = 4

Q alone can do the job in 4 Days

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