Question

In a same time a can work 50% more than



b.B alone can complete a work in 20 hours.In how many hours a and b complete worke together

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
A can work 50% more than B

B alone can complete a work in 20 Hrs.

Time taken by A and B working together to complete the work= ? Hrs

$\underline{\large{\textbf{Step-1:}}}$
Find the ratio of Efficiency of A to B.

Let Efficiency of A be 100

Ratio of Efficiency of A to B $= 100 : (100+50) = 100 : 150 = 2 : 3$

$\underline{\large{\textbf{Step-2:}}}$
Find the ratio of time taken in completing the work by A and B

Ratio of time taken in completing the work by A and B can be obtained by interchanging the antecedent and consequent of the ratio of Efficiency of A to B.
(Inother words, i.e., inverse ratio of Efficiency of A to B.)

Ratio of time taken in completing the work by A and B = 3 : 2

$\underline{\large{\textbf{Step-3:}}}$
Find the time taken by A alone to complete the work.

Let time taken by A alone in completing the work be x days

$\implies 3:2 = x : 20$

From the means - extremes property of proportion,
Product of Extremes = Product of Means

$\implies 20 \times 3 = 2 \times x$

$\implies 2x = 60$

$\implies x = 30$

$\therefore$ Time taken by A alone in completing the work = 30 Hrs

$\underline{\large{\textbf{Step-4:}}}$
Find the work done by A and B in one day

Total work = HCF(time taken by A in completing the work, time taken by B in completing the work)

$\therefore$ Total work = HCF(20, 30) = 10 Units.

Now ,
A requires 20 Hrs to do 30 Units

In one day, A will do $\frac{30}{20} = 1\, \frac{1}{2}\: Units$

B requires 30 Hrs to do 30 Units

In one day, B will do $\frac{30}{30} = 1\: Units$

$\underline{\large{\textbf{Step-4:}}}$
Find the work done by A and B in one Hour

Working together, A and B will do $(1 + 1\, \frac{1}{2}) = \frac{3}{2}$ units

$\underline{\large{\textbf{Step-4:}}}$
Find the time taken by A and B working together for 10 units.

For 10 Units ,
Time taken by A and B = $\dfrac{10}{(\frac{3}{2})} = \dfrac{20}{3} = 6\, \frac{2}{3}\: Hrs$

$Therefore$

$\bigstar$A and B takes $6\, \frac{2}{3}\: Hrs$ working together.

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