A and B alone can complete a piece of work in X and Y days respectively. A and B together can do the same work in 24 days. If A alone does (\({1\over 3}\))^{rd} of the work and B alone does remaining (\({2 \over 3}\))^{rd} of the work and thus the work gets completed in \(46 {2 \over 3}\) days, then in how many days B alone can complete the whole work? (Given: (X – Y) > 15)

## Answer

Correct Answer : d ) 40 days

Explanation :A alone can complete a piece of work in X days

So, part of the work done by A in one day = \({1\over X}\)

B alone can complete a piece of work in Y days

So, part of the work done by B in one day = \({1\over Y}\)

According to question,

\({1\over X} +{1\over Y}={1\over 24}\)

As A complete whole work in X days

So, A will complete the \(({1\over 3})\)^{rd }of the work in ⇒ \(({X\over 3})\)days

As, B complete whole work in Y days

So, B will complete \(({2\over 3})\)^{rd} of the work in ⇒ \({2Y\over 3}\)days

According to the question, A alone does of the work and B alone does remaining \(({2\over 3})\)^{rd} of the work and thus the work gets completed in \(46{2\over 3}\)days

Thus,

\( {X \over 3}+ {2Y \over 3}= 46{2\over 3}\)

⇒X+2Y=140……2

Comparing equation (1) and (2) we get,

\({1 \over (140-2Y)}+{1 \over Y}={1 \over 24}\)

\({Y+140-2Y \over (140-2Y)(Y)}={1 \over 24}\)

140 * 24 – 24Y = 140Y – 2Y^{2}

2Y^{2} – 164Y + 24 * 140 = 0

Solving the above equation for Y we get

Y = 42, 40

Putting the value of Y in equation (2) we get

(X, Y) = (56, 42); (60, 40)

Now,

For first pair i.e. (X, Y) = (56, 42)

X – Y = 14

Thus, the given condition X – Y > 15 fails here.

For second pair i.e. (X, Y) = (60, 40)

X – Y = 20

Therefore, B can complete the whole work in 40 days.

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2& 3, UPSC CDS, UPSC NDA, etc.

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