Question

Tunga takes 3 more days than the number of days taken by Gangadevi to complete a piece of work.if both tunga and Gangadevi together can complete the same work in 2 days,in how many days tunga alone can complete the work?

Answer 1

6 days

Explanation:

G= the time, expressed in days, that Gangadevi takes to complete one piece (unit) of work.
T = the time, expressed in days, that Tunga takes to complete one piece (unit) of work and we know that
`T = G+3`

`1/G` is Gangadevi's working speed, expressed in units per day
`1/T` is Tunga's working speed, expressed in units per day

When they work together, it takes them 2 days to create a unit, so their combined speed is `1/T + 1/G = 1/2`, expressed in units per day

substituting `T = G+3` in the equation above and solving towards a simple quadric equation gives:

`1/(G+3) + 1/G = 1/2`

`2xxGxx(1) + 2xx(G+3)xx(1) = (Gxx(G+3))`

`4G+6 = G^2 + 3G`

`G^2 - G -6=0`

Factoring with `a = 1, b= -1 and c = -6` gives:
according to the factoring formula
`x1,2 = (-b+- sqrt(b^2-4xxaxxc))/(2xxa)`

gives
`x1= (1-sqrt(25))/2 = -2`
and
`x2= (1+sqrt(25))/2 = 3`
as two solutions for G (the nr of days it takes Gangadevi to finish one unit of work)

only x2 is a valid solution as x1 is a negative value.

so: G=3, meaning that T=G+3 = 6