Aptitude - Time and Work - Discussion

A and B can do a work in 28 days. A is 7/4 efficient than B. If B done the work in how many days. Please explain friends.

Efficiency ratio is 7:4.

Time ratio is 4:7.

Work ratio is inversely proportional to time ratio.

Here A is more efficient so A's time is less, B is less efficient than a so B take more time than A.

So both take 28 days (7 + 4) 11 ---- 28.

11/7*28 = 11*4 = 44 days.

So answer is 44 days.

How to come A is 7/4 times efficient than B?

Here efficiency is given so we have to change efficiency into time but in this this why the efficiency is not change I want to know the reason please explain it. 7/4:1=7x:4x this is efficiency 4x:7x this is the time in this question why we are not change the efficiency into time.

Why 7/4 explain guys?

Given, A+B = 1/7 ------(1).

And A = 7/4B (A is 13/4 times as efficient as B).

Sub A = 7/4B in (1).

We get B = 4/77---- (2).

Then Sub (2) in (1).

We get A = 1/11 (which means A can complete work in 11 days).

a : b if work ratio is 7 : 4 then time ratio is 4 : 7.

Let a takes 4x and b takes 7x days.

So 1 days total work 1/4x + 1/7x = 1/7.

So here we get x = 11/4.

So a takes 4x = 4*11/4 = 11 days.

How come efficiency is directly proportional to the no of days worked?

Given: A is 7/4 times as efficient as B.

A:B = 7/4:1 => A:B = 7:4(the ratio is in terms of efficiency).

As we know that efficiency is indirectly porporational time taken to finish the work done.

A:B = 4:7(the ratio is in terms of time taken to finish the work).

A+B = 7 (this is the time taken to finish the work together).
=> B = 7-A substituting in above equation.
=> A:(7-A) = 4:7.
=> A/7-A = 4/7.
=> 7A = 4(7-A).
=> 7A = 28-4A
=> 7A+4A = 28.
=> 11A = 28.
=> A = 28/11.
=> A = 2 6/11 is the answer.

Step 1.
One day work of A and B, (A + B) = 1/7 ----> (1)

Step 2.
A:B =4:7, according to time not work.

Step 3.
Let assume A and B one day work be 1/4x and 1/7x.
Now, put the value of A and B in equation (1).

A + B = 1/4x + 1/7x.
=1/7 and getting x value as 11/4.

Step 4.
Put the value of x in A's 1-day work, 4x = 4X(11/4) =11.