Aptitude - Time and Work - Discussion

Given X + Y =30.

They never mentioned any efficiency (like B is twice as good).

Assume that they are equal efficiency.

So A Did only 16 days work and B completed remaining work in 44 days.

Therefore total work of B is 44 + 16 = 60.

Total work of A is also 60.

I will tell the simplest way. From this question, it's clear that A worked for 16 days and B worked for 44 days so 1/30 * 16 + 1/B * 28 = 1. So we get B = 60.

A+B completes work in 30 days, so,

=>unit of work done by both A and B in 1 day = 1/30,
Consider that total work done by both A and B = 30 units,
So,in 1 day = 1 unit work is done,
Since 1 day = 1 unit of work then A do 16 units of work,
Remaining work = 30-16 = 14 units,
This 14 units of work is done by B in remaining 28 days(44 days-16 days).

If we see read the question we get that "the total number of days required by B to complete the total 30 units" is asked.
So we do like this,
for 28 days = 14 units,
x days = 30 units,
we get 14*x = 28 * 30,
=>x = 28*30/14,
=>x=60 days.

How we are getting 1 in the equation 16x+44y please Explain.

Total work is equal to the LCM of 30, 16 & 44. ie 2640.

B finished the work in 2640/ 44 = 60 days.

1/30 - 1/16 = 7/240

2*1 / 44 = 1/22

7/240 - 1/22 = 43/2640

Is there a formula?

My method:- Mixture

A -------------- B
16 -------------- 44
30 --------------
14 : 14
1 : 1

So, B completed the whole work( means A's work +B's work alone)=(16 x1 +44 x 1) = 60 days.

A + b=30.
Let the efficiency of a and b is 1.
Then total work will be 30*2=60.
A did 16 work then remaining work is,

60-16=44 which will be completed by b in 44 days so B's actual efficiency is 1 so B will finish 60 work in 60 days.

A's 1 day work = x.
B's 1 day work = y.

They work together x+y= 1/30; x = 1/30-y.
A having work for 16 days and B finishes remaining work alone 44 days 16x+44y = 1.

16*(1/30-y)+ 44y =1.
16/30-16y + 44y =1.
16/30 -28y =1.
28y= 1-16/30.
28y=7/15.
y=7/15*28.
y=1/60.

B's alone do the work in = 1/60 days = 60days.