Here is the problem from Question pack one
Last month Grace worked and was paid for, a total of x hours. Some of the hours were on day shift & some on night shift.Her hourly pay is 20% higher fro the night shift then the day shift. How many hours did Grace work on the day shift last month
1) X =55
2) Grace's pay for the hours she worked on dayshift last month was exactly 50% of her total gross pay for last month
Using three variables i.e one for day shift hours the other i.e X for total hours & the hourly wage rate I am able to solve this problem but it takes over 4 minutes. Is there any shorter way of solving this
well, you should be able to tell pretty quickly that the two individual statements are insufficient.
1/ these 55 hours could be divided up in any way at all.
2/ this is just a ratio, with no indication of any absolute number of hours. so it's going to determine, at most, some ratio
of day- to night-shift hours, but it won't let you figure an actual number
(as required in the problem).
so, let's combine the statements.
no need for three variables. we have a total of 55 hours, so you can split that into x hours on the day shift and (55 - x) hours on the night shift.
for the wage, let's say W dollars/hour for the day shift. then the night shift wage is 20% more than this, or 1.2W per hour. (you can actually pick a number for the wage here, but picking constant values is a risky proposition in DS problems.)
so you have x hours at W dollars/hour, and (55 - x) hours at 1.2W dollars/hour.
that's a total of xW + (55 - x)(1.2W) = xW + 66W - 1.2xW
= 66W - 0.2xW dollars.
the pay for day shift is xW dollars.
xW = 50% of (66W - 0.2xW)
xW = 33W - 0.1xW
x = 33 - 0.1x
this is an equation you can solve, so, you're done. (c).