Question

2) 100
D04
A is 1.5 times as efficient as B, and C takes halftime as compared to A. IF A and B take 2(2/5) days to
complete half of the work then find the time taken by A and C together to complete the whole work.
1)2 1/3 days 2) 3 1/3 days 3) 3 11/3 days 4) 12/3 days 5)23 days​

Answer 1

The time taken by A and C together to complete the whole work is 2(2/3) days.

Step-by-step explanation:

A is given as 1.5 times efficient than B i.e., (Efficiency A)/(Efficiency B) = 3/2

Since Efficiency ∝ [1/Time period]

So, let’s assume the time taken by B alone be “x days”, then the time taken by A alone will be “2x/3” days.

So,  

Work done by A in 1 day = 1/x

Work done by B in 1 day = 3/2x

It is also given that,

If ½ the work is done by A and B in 2$\frac{2}{5}$ days = (12/5) days

Then, 1 complete work will be done in = (12/5) * 2 = (24/5) days

Therefore, we have  

1/x + 3/2x = 5/24

⇒ (2x + 3x)/2x² = 5/24

⇒ 5x / 2x² = 5/24

⇒ 5/2x = 5/24

⇒ x = 12  

∴ Time taken by A alone = 2x/3 = (2*12)/3 = 8 days

And  

Time taken by C alone = ½ * time taken by A = ½ * 8 = 4 days

Now,

The fraction of work done by A and C together in 1 day is,

= 1/8 + ¼

= (1+2)/8

= 3/8

Thus, A and C can together complete the whole work in 8/3 days or 2 $\frac{2}{3}$ days.

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