Aptitude - Time and Work - Discussion

A and B collectively can do the work in 7 days.
so their one day work is 1/7.

A+B = 1/7-------(1).
A is 7/4 times efficient than B which means.

A = (7/4)B ----------(2).
or
B = (4/7)A ------------(2).

Put 2 int 1 eq,
A+(4/7)A = 1/7.
A(11/7) = 1/7.

SO,
A CAN COMPLETE THE PIECE OF WORK IN 11 DAYS.

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.

A's working capacity = X.
B's working capacity = Y.

Given, X + Y = 1/30 ................equation(1).

Also, X = 7/4 Y

i.e.. Y= 4/7 X .................equation (2).

PUTTING Y=4/7X from eqtn (2) in Eqtn(1), we get,

X= 1/11.

i.e.. A working capacity is 1/11( interpretation: "A" can do 1 work in 11 days).

A is 7/4 efficient than B means A=7/4B =>B=4/7A.

A and B together can complete the work in 7 days.
[i.e.Time is directly proportional to work => 7days=work => 1 day=1/7th work].

So,

A + B = 1/7.
A + 4/7A= 1/7.
11/7A = 1/7.
A = 1/11.

Hence, A alone can work for 11 days.

GIVEN : A=7/4B, THEREFORE B = 4/7A.

A + B = 1/7.
A + 4/7A = 1/7.
11/7A = 1/7.
A = I/7*7/11 = 1/11.

Hence 11 days.
Hope this is a correct way.

How we get A =7/4? Please help me.

@Raj.

They given 1*3/4 in example after solving it we get 7/4(4*1+3).

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?