could you pls check the stat 1) , is it 34 the amount or 3/4th the amount or sumthin else , coz it is not clear the way it is stated
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let individual rates be R & S respectively, we need to find R

stat1 ) given that S = \(\frac{3}{4}\) R, but we do not more information to cal respective values , hence Not Suff

stat2) given together they both take 12 min , so lets put it the work time equation

\(\frac{1}{S}\)+\(\frac{1}{R}\) =\(1/12\) ==> \(\frac{R+X}{RS}\) = \(\frac{1}{12}\)

still not suff as we two unknowns and 1 eq

Stat1) + stat2) , we can use stat1) and put the value S in the eq of stat 2) , and we can cal R , Hence suff

C

Just for calculations, R= 28 mins
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Solution

Given:

• Machine R and machine S work at their respective constant rates

To find:

• The time taken by machine R, working alone, to complete a certain job

Analysing Statement 1

• As per the information given in statement 1, the amount of time that it takes machine S, working alone, to complete the job is \(\frac{3}{4}\) the amount of time that it takes machine R, working alone, to complete the job
• From this statement, if we want to find out the time taken by R individually to complete the job, we must know the time taken by S individually to complete the job

o As no information is given about the time taken by S to complete the job, we can’t find the time taken by R to complete the job

Hence, statement 1 is not sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, machine R and machine S, working together, take 12 minutes to complete the job
• From this statement, if we want to find out the time taken by R to complete the job, we must know either the time taken by S to complete the job or their ratio of efficiency

o As none of the information are provided, we cannot get the answer

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Combining both the statements, we can write:

• S takes \(\frac{3}{4}\) of the time taken by R to complete the job, while working alone
• R and S together take 12 minutes to complete the job

If we assume R takes x minutes to complete the job, then S would have taken \(\frac{3x}{4}\) minutes to complete the job

• Therefore, we can write \(\frac{1}{x} + \frac{4}{3x} = \frac{1}{12}\)
• We can find the value of x from this given equation

Hence, the correct answer is option C.

Answer: C
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