Solution
Steps 1 & 2: Understand Question and Draw InferencesGiven:• Let the rate of production for machines A, B and C be a, b and c units of work per hour
• Let the total amount of work required to produce the batch of balls be W
• Time to do W work when A and B operate simultaneously is 4 hour 48 min
o \(\frac{\mathrm W}{\mathrm a+\mathrm b}=4\;\mathrm{hour}\;48\min=4\frac{48}{60}=4\frac45=\frac{24}5\mathrm{hours}\)
o So, \(\mathrm a+\mathrm b=\frac{5\mathrm W}{24}\) . . . (I)
To find: Time T to do W work when A and C operate simultaneously
• \(\mathrm T=\frac{\mathrm W}{\mathrm a+\mathrm c}\)
Thus, to find the value of T, we need to find the sum a + c in terms of W
Step 3: Analyze Statement 1 independently(1) Machines A, B and C operating simultaneously can produce the same batch of balls in \(\frac{24}{11}\) hours
•\(\frac{\mathrm W}{\mathrm a+\mathrm b+\mathrm c}=\frac{24}{11}\)
• So, \(\mathrm a+\mathrm b+\mathrm c=\frac{11\mathrm W}{24}\) . . . (II)
• From (I) and (II),
o \(\mathrm c=\frac{6\mathrm W}{24}=\frac{\mathrm W}4\) . . . (III)
• Thus, we now know c in terms of W but we don’t yet know a in terms of W
Not sufficient.Step 4: Analyze Statement 2 independently(2) Machine B operating alone takes 50 percent more time to produce the same batch of balls than Machine A operating alone
• Time taken by machine B operating alone to produce same batch of balls =\(\left(1+\frac{50}{100}\right)\ast\;\) Time taken by machine A working alone to produce same batch of balls
\(\begin{array}{l}\frac{\mathrm W}{\mathrm b}=\left(1+\frac{50}{100}\right)\left(\frac{\mathrm W}{\mathrm a}\right)\\\Rightarrow\frac1{\mathrm b}=\frac3{2\mathrm a}\\\Rightarrow\mathrm b=\frac{2\mathrm a}3...(\mathrm{IV})\end{array}\)
• From (I) and (IV),
\(\begin{array}{l}\mathrm a+\frac{2\mathrm a}3=\frac{5\mathrm W}{24}\\\Rightarrow\frac{5\mathrm a}3=\frac{5\mathrm W}{24}\\\Rightarrow\mathrm a=\frac{\mathrm W}8\;....(\mathrm V)\end{array}\)
We now know the value of a in terms of W but not of c.
Not sufficient.
Step 5: Analyze Both Statements Together (if needed)
• From Statement 1: \(\;\mathrm c=\frac{\mathrm W}4\)
• From Statement 2: \(\;\mathrm a=\frac{\mathrm W}8\)
• Therefore, \(\mathrm T=\frac{\mathrm W}{\frac{\mathrm W}8+\frac{\mathrm W}4}\)
In this expression, W will cancel from the numerator and denominator. Therefore, we will get a unique value of T.
Thus, the two statements together are sufficient to answer the question.
Answer: Option CThanks,
Saquib
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