Aptitude - Time and Work - Discussion

a is not equal to 30...dude
a+b+c=1/16
b+c=1/24
solving above eqn
a+b+c-(b+c)=1/16-1/24..........

Hi friends, let me explain one simple method to solve this problem.

It is lengthy process, but you will understand easily.

(a+b)'s 1 day work = 1/30.
(b+c)'s 1 day work = 1/24
(c+a)'s 1 day work = 1/20.

solving that equations we will get
a =1/48 , b = 7/240 , c = 1/80

now,
(a+b+c)'s one day work = 1/48 + 7/240 + 1/80.
= 15/240.
= 1/16.

i.e,
(a+b+c)'s 10 days work = 10/16
=5/8

remaining work = (1- 5/8)
= 3/8

3/8 portion of work is completed by a alone....

now,

a completes 1/48 portion of work in 1 day....
a completes 3/8 portion of work in _ days.....?

1/48------> 1
3/8-------> x

by cross multyplying,we will get

x /48 = 3/8

x = 18..

So, A alone can complete the work in 18 days.

We want short cut please anybody solve this shortcut method. Why taken 2 (a+b+C).

2(A + B + C)'s 1 day's work = 1/8.

Then (A + B + C)'s 1 day's work = 2/8.

How come it is 1/16 ?

While calculating A's 1days work, (1/16-1/24) =1/48.

Why we are taking 1/24 ?

A+B=1/30 AND B+C=1/24 AND C+A=1/20.

As per question all work together means : a+b+b+c+c+a=2a+2b+2c;

2 is common factor so we can write it as 2(a+b+c).

2(a+b+c) 1 days work =1/8 then a+b+c 1 day work=1/16 then a's 1 day work=1/16-1/24=1/48 then in 10 days a+b+c can do 10/16 work now remaining work=1-10/16=3/8 now in 48 days a can do 1 work then 3/8 work a can do in 48*3/8=18.

How we wrote the third step?

@Bikash.

Brilliant way, keep it up.

What @Naveen kumar said is good and really simple to understand even though it's somewhat long. But no problem. Thank you dude.