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?

1 Answer
Jun 15, 2018

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