Aptitude - Time and Work - Discussion

Taniya can do 25% more than Sakshi
i.e., Taniya = 100%+25% = 125%of Sakshi
Sakshi 1 day of work is 1/20 then 125% of 1/20
i.e., 1.25*(1/20) = 1/16 in one day for Taniya
So, the work will be completed in 16 days.

Yes, you are correct @Okley.

Why can't 15 be the answer?
25%of 20=5 subtracts from 20 then gets 15, right?

Sakshi can do a piece of work in 20 days and Tanya is 25% more efficient than Sakshi that means

125% of Work by Sakshi in ------------> 20 days.
100% of Work by Tanya ---------------> x.


By Cross Multiplication we get;

125% * x = 100% * 20,
=> (125/100) * x = (100/100) * 20,
=> x = (100/125) * (100/100) * 20,

After Cancellation You'll get Result as 16 days.

25% efficient means Tanya takes 15 days.
Both 1 day work=1/20+1/15=7/60.
Tanya work=7/60-1/20=1/15.
Why can't the answer be 15?

Let us solve it easily:

So, Tanya is 25% more efficient than Shaksi which means Tanya is 100% then Sakshi will be 125%
Now: Sakshi:125--> 20 days
Tanya :100-->x.
By cross multiply(x)-->x=20*100/125.
= 16days.

@All.

Here Tanya is 25% more efficient than Sakshi. So why can't we take Tanya as 100 and Sakshi as 75. It can be understood from the basic concept of percentages that if A is 25% more than B, B is how much percent less than A and that will never be 25.

Let B=100 => A=125. Difference= 25. How much is B less than A = (25/125)*100 = 20%. The change is to be taken from A i.e 125 and not 100.

Similarly, if Tanya is 25% more efficient than Sakshi, then Sakshi is 20% less efficient than Tanya and not 25%.

So going by this, if you take 80 instead of 75, you will get the same answer which is also the only correct answer.

@Oakley.

Efficiency: When we say Tanya is 25% more efficient than Sakshi, it means Tanya can do 25% more work in the same amount of time compared to Sakshi. This directly affects the number of days she will take to complete the work.

Efficiency does not directly translate to days: If Tanya is 25% more efficient, it doesn't mean she will take 25% fewer days. Instead, her work rate is 25% higher.

Solve by the Trick:

100 * M/100 + X.
Here, M = day.
X= efficiency.
Therefore:

100 * 20/100 + 25,
2000/125,
16 days.

(SAKSHI) 125%=20,
(TANYA) 100%= x,
125*x = 20*100,
x = (20*100)/125,
x = 16 days.

As Sakshi can do 1/20 per day, Tanya can do 25% more per day than Sakshi.
So, [(1/20)+(1/20)*(25/100)].

i.e. 5/80 i.e 1/16 i.e 16 days.