Aptitude - Time and Work - Discussion

20. 

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

[A]. 15
[B]. 16
[C]. 18
[D]. 25

Answer: Option B

Explanation:

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x    x = 4 x 20
5

x = 16 days.

Hence, Tanya takes 16 days to complete the work.


Kamlesh Jaiswal said: (Sep 2, 2010)  
The given answer is correct.

Sakshi's one day work=1/20
Tanya's one day work =(1/20 + 25% of 1/20) = 1/20+1/80 = 1/16.

So Tanya can complete the work in 16 days.

Siddharth said: (Sep 23, 2010)  
Thanks kamal you are right.

Sandeep said: (Jan 8, 2011)  
If tanya is 25% more efficient than sakshi (whic means tanya>sakshi) then how cum the ratio between sakshi n tanya is 125:100 it should be 100:125 right?.

Sujith said: (Jan 30, 2011)  
Tanya is 25% more efficient than Sakshi. Then ratio should be 3:4 rite ?.

Sundar said: (Apr 16, 2011)  
@Sujith and @Sandeep

You are wrong.

The given ratio is about "TIME TAKEN" not the ratio of work done.

If Tanya is more efficient (25%) than Sakshi - means Tanya will take less time than Sakshi to complete the work.

We can say the same thing in another way, i.e., Sakshi is 25% INEFFICIENT than Tanya. So, if Tanya takes 100 hours to complete a task then Sakshi will take 125 hours (25% extra than Tanya) to complete the same task.

So, time taken by
Tanya = 100 hours ,
Sakshi = 125 hours.

Therefore, Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

This is what the first line in the given explanation.

Hope this will help you. Have a nice day!

Kiran Joy said: (Jun 16, 2011)  
Can't we take time taken by tanya and sakshi as 75:100.

Deepti said: (Jun 27, 2011)  
Thanks sundar that solves so many other related problems.

Chandu said: (Aug 3, 2011)  
5 : 4 :: 20 : x

Can you explain the meaning of the above line?

Vamshidhar Reddy said: (Sep 6, 2011)  
25% efficient(so one takes 100 days means second person takes 75days[just 75%of 100])

here one takes 20 days
so other takes 20*(75/100)=15 days

Preethy said: (Sep 14, 2011)  
I too get the answer as 15 days. Since 25% of 20 is 5 we have to subtract like 20-5=15 rite? but how the answer is 16?

Xyz said: (Oct 4, 2011)  
Thanks Kamlesh !!!

Samar said: (Nov 26, 2011)  
20*0.25=5
subtract 5 from 20
20-5=15Ans

I also get the answer 15
I did not understand how the answer is 16.

Harshit said: (Dec 14, 2011)  
@Vamshidar reddy, Preethy& Samar;.

The answer 16 is justified.

Given that Tanya is more efficient than Sakshi. So, Tanya will take less time to complete the work.

If Tanya is 25% more efficient than Sakshi, it is not nessesary.

That Tanya will complete the work in 25% of the days less than Sakshi.

Satya Vaag said: (Jan 18, 2012)  
Thanks kamlesh.

Shawisk said: (Jun 20, 2012)  
Read carefully

for tanya & sakshi, the actual ratio is 100:75=4:3

bcz if tanya do same work complete @ 100% in x days
then sakshi can complete only 75% of that work in x days

so keep it in mind

Pandian said: (Aug 30, 2012)  
Sakshi done a work in 20 days is 100%
Tanya more power is 25%
So she done work in minimum days
So 25% of 20 days is 4
So tanya done work in 20-4 = 16 days.

Eby said: (Sep 28, 2012)  
Tanya =125% of Sakshi
Sakshi 1 day work =1/20
So
Tanya =(125/100)*(1/20)
=(5/4)*(1/20)
=(1/4)*(1/4)
=(1/16)
=16 days

K Verma said: (Dec 11, 2012)  
Tanya is 25% more efficient than Sakshi.

Tanya is 125.

Sakshi is 100.

Ratio of efficiency is 5:4.

So, ratio of time will be 4:5.

Given, Sakshi can do work in 20 days means 5*4=20.

In the same way for Tanya 4*4=16.

Answer-16 days.

Akram said: (Dec 19, 2012)  
x:y::p:q.

Product of mean = product of extreme.
..i.e.. y*p = x*q.
y*p/x*q = 1.

Same way : 5:4::20:x
4*20/5 = x
4*4 = x
x = 16.

Pankaj said: (Jul 20, 2013)  
I too get the answer as 15 days. Since 25% of 20 is 5 we have to subtract like 20-5 = 15 right? but how the answer is 16?

Soumil said: (Aug 10, 2013)  
The ratio should be 100:75::20:x, not 125:100::20:x.

San said: (Aug 19, 2013)  
Efficiency is : (1/Number of total days to complete a work).

So, efficiency of sakshy = 1/20.

And,efficiency of Tanya = 1/20 + 25% of (1/20).
Which is,
1/16.

So, Tanya will complete in 16 days.

Roji said: (Oct 3, 2013)  
Hi friends,

Why can't we do in this manner?

Sakshi can done in 20 days i.e.,100%.

Where as, Tanya is x days i.e., 125%.

By cross multiplication,

x = (125*20)/100 = 25.

Answer we get 25.

So, am I wrong?

Already this type of process done in 17th sum but here it is not working yar.

Dhiman Saab said: (Dec 18, 2013)  
@Chandu.

It means 5:4 is known 125:100.
:: may mean equal to
20 here is the number of days taken by Sakshi and we are supposing x to be the days taken by Tanya.

Sai said: (Jan 8, 2014)  
Tanya's one day work =(1/20 + 25% of 1/20) = 1/20+1/80 = 1/16 once explain the equation.

Sandeep said: (Jan 22, 2014)  
(1/20 + 25% of 1/20).
Here 25 % of 1/20 is 1/5.

Then add,
(1/20+1/5), we get,
(1+4/20).

Then we get 1/4.

Above we got 4 days, then subtract 20 from 4
20-4 = 16.

Shravani said: (Jan 25, 2014)  
If tanya is 25% more efficient than sakshi (which means tanya>sakshi) then how cum the ratio between sakshi n tanya is 125:100 it should be 100:125 right?.

Ramesh said: (Mar 8, 2014)  
Sakshi's one day work is 1/20.
Tanya is 25% of sakshi it means 1/20+25%1/20.

= (1/20+25/100*1/20).
= (1/20+1/80).
= 1/16 for one day.

So 16 days to do total work.

Iqbal Sofi said: (Mar 8, 2014)  
It should be 15, because the 25% reduction of 20 is 15.

Manjula said: (May 27, 2014)  
Sakshi working days in 20 days means 100%.
Tanya working days ?

100%-75% = 25%

So 20*25/125 = 4.
20 days - 4 = 16 days.

Pavan said: (Aug 2, 2014)  
Here question starts with sakshi so we must take s=100.

Then 25% eff so T=75.
Then the ratio we get is 3:4.

Answer will be 15.
How can it be 16.

Can anyone please?

Anshu said: (Aug 5, 2014)  
Hey,

You can understand it like this.
As we know working efficiency of sakshi is 1/20.
And working efficiency of tanya is 25% greater.

So tanya eff = 1/20*(125/100)=1/16.

Hence time 16 days.

Geetha said: (Aug 10, 2014)  
Give a brief explain how 125:100 come?

Jasmin said: (Oct 5, 2014)  
Can you explain me chain rule please?

5:4 :: 20:x.

Aisha said: (Jan 27, 2015)  
Sakshi is doing work with x efficiency.

Tanya is doing work with x+25% of x efficiency.

Sakshi = x work.

Tanya = x+25/100x+125x/100 = 5/4x work.

ATQ,

Sakshi is taking 20 days means x ----> 20 days.

5/4x ----> 20 x 4/5 = 16 days.

Deepa said: (Feb 3, 2015)  
20-25%[20] = 15 days.

Jai said: (Mar 7, 2015)  
Hey, how come it is 16?

If Tanya takes 16 days to complete, then it means Sakshi is 25% slower than Tanya. But we have calculate Tanya's time who is 25% faster than Sakshi.

So I reckon it should be 15. Please correct me if I am wrong.

Kundan said: (Mar 18, 2015)  
Tanya does 25% efficient work. What does this mean? This means that the work that Sakshi completes is 100% and Tanya does the same work but 125%. So see efficiency as the greater percentage of work being done by Tanya 125% is greater than 100%.

For example if a does 20 units of work in 5 hrs and b does 40 units of work in 5 hrs. Then 1 hr work of A and B is 4 and 8 respectively. What does this mean? It means that B is doing more work in same no of hrs.

Now consider it as B was doing 40 units of work in 5 hrs. So what is his time for 1 unit of work? its 5/40. i.e 1/8! and similarly for A it is 1/4. So in respect of timing who is fast or efficient? Its certainly B because 1/8 is smaller than 1/4!

Priya said: (Mar 28, 2015)  
Nothing to do all this just simple calculation in question it is given Tanya is 25% more efficient than Sakshi which do in 20 days.

So Tanya will do 125/100*1/20 = 4 days.

Jitendra said: (Apr 15, 2015)  
Let Sakshi completes the whole work = 100 days.

Then Tanya will complete it = 75 days.

Now, 100 = 20.

1 = 20/100 = 1/5.

75 = (1/5) *75 = 15 days.

So answer should be 15 days.

Jitendra said: (Apr 15, 2015)  
Why we should consider 125 and 100.

If we consider that Sakshi 100 and Tanya 75 then,

100 : 75 :: 20 : x.

= 100/75 = 20/x.

=> x = 15 days.

Sanjoy said: (Apr 16, 2015)  
100T = 125S, 20S = 1, consider x day required for Tania.

4T = 5S, S = 1/20, Tx =1.
4T = 5*1/20 1/16x = 1.

4T = 1/4 x = 16.
T = 1/16.

So Tania required 16days to complete the work.

Vijayalakshmi R said: (May 17, 2015)  
S can do a work in 20 days so, s=1/20;

T can do a work 25% more efficient than S.

So, T = 1/20 + (25/100*1/20).

Finally we got T = 1/16.

So 16 is the correct answer.

I am sure about my answer so don't confuse, it may be 25 or other else.

Vamsi said: (Jun 26, 2015)  
If Tanya is 25% more efficient than Sakshi, then as 25% of 20 is 5. Tanya should complete the work in 15 days not 16 days.

Devi Prasad said: (Sep 2, 2015)  
Their is mixed view of this question but we got both the answer correctly.

Raghu said: (Oct 13, 2015)  
The answer is 15 let me tell you.

Tanya is 25% efficient than Sakshi.

If Sakshi do a work in 24 hours then Tanya will do in 18 hours because 12 is 50% of 24. 6 is 25% of 24.

So Tanya take 6 hours less time than Sakshi, so reduce 6 hours in every day upto 20 days 6 x 20 = 120 i.e 5 days.

20 days - 5 days = 15 days.

Sonu Jangra said: (Oct 13, 2015)  
Sakshi do 1 day's the work = 1/20.

Now, Tanya do the work 25% more efficient than Sakshi = 1/20*25/100 = 1/80.

So, Tanya will do the total work = 1/20+1/80 = 5/80 = 1/16.

So 1*16/1 = 16 days.

Pankaj said: (Oct 17, 2015)  
Answer will be 25.

If the ratio taken is T:S::T:S.

125:100::X:20.

5:4::X:20 = 25.

x is no. of days taken by Tanya complete a work.

Subhasis said: (Feb 4, 2016)  
What if I think tanaya takes 75 days and sakshi takes 100 days, then answer will be 15 days.

Suresh Ks said: (Mar 19, 2016)  
Hi friends I agree your answer is 16 based on your methods.

So please let me know how many days Tanya takes if she is 50% more efficient than sakshi based on your methods.

Ashwini said: (Jun 7, 2016)  
According to me, it should be;

Tanya is 25% efficient than Sakshi so that means she finishes work taking 25% less time.

So, 20 - 25 * 20, then finally we get 15 days.

Tathagata said: (Jun 13, 2016)  
@Ashwini you are right. If you see a previous sum. If you do it in the same way it will have the same answer!

Shadab Akhtar said: (Jun 15, 2016)  
Sakshi = 1/20 (given).
Tanya = (125/100) * Sakshi (Tanya is 25% more efficient than Sakshi).
Tanya= (125/100) * 1/20.
= 1/16.

Hence, Tanya does the same piece of work in 16 days.

Narayan said: (Aug 10, 2016)  
Let the ans is 15 then,

Efficiency=((20 - 15)/15) * 100 = 33.33%(wrong).

Take ans as 16 then,
Efficiency = ((20 - 16)/16) * 100 = 25%(correct).

Santosh said: (Sep 18, 2016)  
Thanks @Kamlesh.

Bulu said: (Sep 22, 2016)  
Shaki = 20 days,

Tanya = 25% more efficient,

So that 25% of 20 = 5,

20 days - 5 days = 15 days.

Aashi Mehta said: (Nov 13, 2016)  
If we solve in accordance with the question then the answer will be 15 I don't know why every body has taken it as 16.

Please tell me.

Ayush said: (Nov 26, 2016)  
@All.

Refer the post of Kamlesh It's quite easy to understand, Thanks @Kamlesh.

Soniya said: (Dec 17, 2016)  
Ratio of work done by Tanya and Sakshi = 125 : 100 = 5 : 4.
Ratio of times taken by Tanya and Sakshi = 4 : 5.
5x = 20days. ( Sakshi can complete the work in 20 days).
x = 4.
So, Tanya can finish the work in 16 days.

Cheenu said: (Dec 22, 2016)  
Can anybody explain this how x = 16 has come from this equation 5:4::20:x?

Moses said: (Mar 1, 2017)  
15 is the answer because we are reducing Sakshi's work time by 25% Hence multiply 20 days by 0.75 which will give 15days.

15 days is definitely the answer.

Epsilon said: (Jul 21, 2017)  
Sakshi does 1 unit in =20Days.

Tanya does (1+1/4)=5/4 unit in = 20Days.
So, Tanya does one unit in=20*4/5 = 16 days,
I think efficiency here is related to the amount of work done.

Sanjay said: (Aug 16, 2017)  
Tanya 1 day =100 unit (make).
Sakshi 1 day =75 unit.
Sakshi 20 days = 1500 unit make ( so this is total work ).

Then tanya make = 1500 / 100 = 15 days.

15 days 1500 unit.

15 --> Can Be Answer.

Mithun said: (Aug 31, 2017)  
[Tanya effective than sakshi [20days] , hence answer should be less than 20days]

Sakshi 125--------->20
Tanya 100-------->?
[cross multiply]
20 x 100 / 125 =16days.

Atul said: (Sep 19, 2017)  
Sakshi cannot be taken as 125, as Sakshi is the reference point here, she must be taken as 100.

So, Tanya becomes 75 (25% more efficient).
Then the ratio becomes 4:3 instated of 5:4.

Sahithikarne said: (Jan 29, 2018)  
25% of 20 is 5 then the answer is 20-5=15. But how it is 16?

Mahesh Neupane said: (Feb 10, 2018)  
Sakshi efficiency is 1/20.
Tanya Efficiency is 25% more than Sakshi.
So, 1/20+(25%of1/20)=16%.

Patrick said: (Feb 11, 2018)  
Sakshi efficiency = 100/20 = 5;
Tanya = 5 x 1.25 = 6.25;

The number of days taken by Tanya to do the same piece of work is: 100/6.25 = 16 days.

Manish Niroti said: (Feb 19, 2018)  
Tanya & sakshi capacity =5:4.
Tanya & Sakshi time taken=4:5.

If Sakshi taking 20 days it means 5 is representing 20 so 20/5 =4,
and multiply 4 with taken by Tanya so you will get 4*4 =16.

Ratio and proportion concept.

Komal Singh said: (May 30, 2018)  
@Sakshi.

If takes 125 times to complete her work in 20 days, Tanya takes 100.

Therefore if we cross multiply to find how much days will Tanya take to complete work.

i.e 125/100*20/? we get 16!

Divyansh said: (Jul 14, 2018)  
I am not getting it how 16?

Let's think this way Sakshi take 20 days which is 240 hours.
25% of 240 = 60.
240 - 60 = 180.
and 180 hours = 15days.

Please can anyone help me.

Sufiyan Ansari said: (Sep 3, 2018)  
See This for those Who do Time and work with LCM..

It is said that Sakshi can do a piece of work in 20 days with her efficiency so we cannot take 25%of 20.

Here it is given 25% more efficient.
So efficiency of Sakhsi : Tanya.

Assume: S:T = 100unit : 125 unit (25%more).

Therefore ,
Total work = 100unit x 20days.
:. Tanya would do the same work in:
Total work/ Tanya efficiency,
:. 100unit x 20/125= 16 days.

Vishal Bhadikar said: (Sep 23, 2018)  
Why not 15 days? Explain..
100%=20 day.
25%=x day.
X = 5 days.

Now take efficient that we need to subtract 20-5 = 15 days.
Explain to me if I am wrong.

Srilatha said: (Oct 8, 2018)  
Sakshi complete the work in 20 days . Tanya is 25% more efficient means;
in 20days 25%=5 days.
it means t complete the work in 5 days earlier.
so 20-5=15 answer.

Then how it comes as 16?

Ahsan Naveed said: (Dec 1, 2018)  
@All.

Tania is 25% more efficient then Sakshi so we can do it like,
Tania=125 units/day, Sakhi = 100 units/day.
As Sakhi done it in 20 days so we can find complete work done,
Total work= 20 * 100 = 2000.

We also have Tania unit work so we will divide total work with Tania unit work,
Tania work= 2000/125 = 16 answer.

Pitambar said: (Jan 22, 2019)  
A certain number of men do a piece of work in 10 days, if there are 10 men less, it will take 10 days more to finish the work. How many men were there originally. Can anyone solve this to find a solution?

Kajal said: (Sep 13, 2019)  
Here (125% of 1/20)=1/16 that means in 16 days.

Ryan said: (Sep 28, 2019)  
@All.

The sentence 'Tanya is 25% more efficient than Sakshi' means Tanya will take 25% less days than Sakshi and not that Sakshi will take 25% more days than Tanya. The answer given assumes the later part which is not correct. Percents work differently for the increase and decrease.

For example, 25% more than 100 is 125. But 25% less than 125 is not a hundred.

The answer would be 16 if the question had been stated as Sakshi is 25% less efficient than Tanya.

Annie said: (Oct 22, 2019)  
Can anyone please compare it with the 17th question?

Leela said: (Nov 4, 2019)  
@Ashan Naveed.

Consider 100 unit by Sakshi
Tanya 125 unit. Y can't we consider Sakshi by 125 days. Tanya in 100 days. Mainly unitary method how can we solve.

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