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Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A alone can do a piece of work in 30 days. If A and B can do the same piece of work in 20 days, then B alone can do the same piece of work in how many days? Quantity II: Two pipes M and N can fill a tank in 15 hours and 20 hours respectively. These pipes are opened alternately and pipes M is opened first, in how many hours, the tank fill-in?

Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A alone can do a piece of work in 30 days. If A and B can do the same piece of work in 20 days, then B alone can do the same piece of work in how many days? Quantity II: Two pipes M and N can fill a tank in 15 hours and 20 hours respectively. These pipes are opened alternately and pipes M is opened first, in how many hours, the tank fill-in? Correct Answer Quantity I > Quantity II

Given:

A can do a piece of work in = 30 days

A and B can do the same piece of work in = 20 days

Concept used:

1/A + 1/B = 1/A + B

Calculation:

Let time taken by B alone be x days

A’s one day work = 1/30

B’s one day work = 1/x

(A + B)’s one day work = 1/20

Now,

1/30 + 1/x = 1/20

⇒ 1/x = 1/20 – 1/30

⇒ 1/x = (3 – 2)/60

⇒ 1/x = 1/60

⇒1/x = 1/60

⇒ x = 60

∴ The Time is taken by B alone will be 60 days

Quantity II:

Given:

Time taken by pipe M = 15 hours

Time taken by pipe N = 20 hours

Calculation:

Let the total capacity of tank be LCM (15, 20) = 60 litres

Now,

Tank filled by M in 1 hour = 60/15

⇒ 4 litre/hour

Tank filled by N in 1 hour = 60/20

⇒ 3 litre/hour

Tank filled by (M + N) in 1 hour = (4 + 3)

⇒ 7 litre/hour

Now,

According to the question,

For first hour pipe M is opened = 4 litre

For second hour pipe N is opened = 3 litre

For third hour pipe M is opened = 4 litre

For fourth hour pipe N is opened = 3 litre

Similarly, So…. On

Now,

We conclude that –

2 hours   =      7 litre

× 8                    × 8

16 hours    =      56 litre

Now,

The remaining work = 60 – 56

⇒ 4 litre

Now,

Again 17th hour M will be opened and fill the remaining tank

⇒ 4/4

⇒ 1 hour

Now,

The tank fills in = (16hour + 1 hour)

⇒ 17 hours

∴ The tank will be fill in 17 hours.

The comparison of both the Result:

∴ Quantity I > Quantity II

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