Problem base on Men at Work?

Question

Soumya Takes 6 days less than the number of days taken by bhagya to complete a piece of work. If both sowmya and Bhagya together can complete the same work in 4 days. In how many days will Bhagya complete the work

Please Explain Clearly

Answer 1

4 days seems like the answer was already given

Answer 2

let S be no of days for sowmyato complete the work

let B be no of days for bhagya to complete the work


sowmya's ONE DAY work is 1/S
bhagya's ONE DAY work is 1/B

since both complete the work in 4 days

1/S + 1/B = 1/4

since sowmya takes 6 days lesser than bhagya

S = B - 6

solving these two


1/(B-6) + 1/B =1/4

(2B - 6 ) / ( B^2 - 6 B) = 1/4

8B - 24 = B^2 - 6 B

B^2 - 14B - 24 = 0

B = 12 ,2
substituting B =2 in the eqn S is negative which is absurd

thus B =12

S =6

Answer 3

lets say soumya completes the work alone in x days and bhagya completes the wor alone in x+6 days they complete the work in 4 days

1/x + 1/(x+6) = 1/4

x+6+x
---------= 1/4
x^2+6x

8x+24=x^2+6x
x^2-2x-24=0
(x-6)(x+4)=0 so x is 6 that mean soumya completes the work alone in 6 days so bhagya completes the work alone x+6=12 in 12 days

Answer 4

Bhagya takes 7 days, Soumya takes 1 day (which is six days less). Combined is eight work days divided by two people, which is four days.

Answer 5

bhagya will complete the job in 5 days