Aptitude - Ratio and Proportion - Discussion

Discussion :: Ratio and Proportion - General Questions (Q.No.2)

2. 

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

[A]. 2 : 5
[B]. 3 : 5
[C]. 4 : 5
[D]. 6 : 7

Answer: Option C

Explanation:

Let the third number be x.

Then, first number = 120% of x = 120x = 6x
100 5

Second number = 150% of x = 150x = 3x
100 2

Ratio of first two numbers = 6x : 3x = 12x : 15x = 4 : 5.
5 2


Ganapathy said: (Jul 7, 2010)  
Let third no be 100.
the first no is 20% more than third so 120
similarly
second no is 50% more than third so 150
just compare
120:150
4:5

Sheetal said: (Jul 29, 2010)  
Suppose the 3rd no is X.
so 1st no will be X*1.2.
&2nd no will be X*1.5.
so the ratio is 1.2:1.5,
Hence 4:5

Ramesh said: (Dec 9, 2010)  
120/100 : 150/100
120:150
12:15
4:5

Xyz said: (Jan 22, 2011)  
20%=1/5
50%=1/2

So ratio should be equal to 1/5:1/2

Ans= 2:5 ?

Ramesh said: (Feb 10, 2011)  
Dear xyz, it is not 20% and 50%, but it is 20% and 50% MORE THAN third number.

If third no is 100, it is 120 and 150
So, 120 : 150
12: 15 or
4:5

Sridhar said: (Feb 23, 2011)  
Why should take the value of third no is 100 only? why not 60, 70, 80.

Sathya said: (Feb 24, 2011)  
Let 3rd no is x
20%of x=(20/100)*x
50%of x=(50/100)*x
1/5x:1/2x
ans=2:5

Suganya.P said: (Jun 13, 2011)  
I do know understand this concepts please explain.

Sumit said: (Jun 24, 2011)  
Let it be of 100. It is most convennience.

Sathi said: (Jul 1, 2011)  
Take A,B,C as three numbers

A is 20% more than C

A=C+20%of C=C+0.2C=1.2C

same way

B=C+50%of(C)=C+0.5C=1.5C

ratio A/B=1.2C/1.5C=4/5

Ans 4/5

Sruthi said: (Jul 4, 2011)  
Sathi's concept is right.

Haseeb Siddiqi said: (Jul 11, 2011)  
Ramesh's method is good and easy.

Naveen said: (Jul 16, 2011)  
Take 10 and 20% more than 10 is 12 and 50% more than 10 is 15 so the ratio is 12:15 which is nothing but 4:5 .

Kunal said: (Sep 4, 2011)  
Why take third number as 100?

Priyabrata Muduli said: (Sep 18, 2011)  
Sathi's concept is right.

Manimekalai.V said: (Sep 22, 2011)  
Ganapathy method is good.

Abhishek said: (Oct 2, 2011)  
I took x:x+20:x+50

then i assumed x+(x+20)+(x+50)=100

3x+70=100
x=10
hence the ration is 30/60
1/2

where did i go wrong?

Sandeep said: (Oct 3, 2011)  
Some one explain why it is 100?

Kushi said: (Oct 13, 2011)  
Thanks sathi.

Ali said: (Nov 4, 2011)  
Hey guys plz don't bother!
let us make it simple...
it was said that first number is 20% more than third number
and second number is 50% more than third number..
now,
we assume the third number is "x".
we all know that "x" means "1x" not just "x"

so 20% more and 50% more than third number means
(20%)+(1x) and (50%)+(1x)
=(0.2)+(1x) and (0.5)+(1x)
=1.2x and 1.5x
now
1.2 : 1.5
let us forget the decimal and assume it 12 : 15
now simplify 12 : 15
i.e divide it by 3.
you'll get 4:5

that's it....

Nidhi said: (Nov 12, 2011)  
Ganapathy you are awsome.

Richa said: (Nov 26, 2011)  
Sathi method is very good.

Gnaneswar said: (Jan 3, 2012)  
Sathi concept is perfect.

Enigma said: (Jan 8, 2012)  
How can one add a costant n a variable?
dats wrong..!
its simply..
x=20/100*z+z
y=50/100*z +z
if z is taken as the third no.. :)

Sasa said: (Jan 13, 2012)  
Ali and ganapathy good work :).

Gitty said: (Feb 1, 2012)  
If you take x as 100 we will get 4:5..agreed. What is the problem in taking x as a variable itself..? Then the answer become 2:5,right..? could anyone please explain ?

Satish Rathnam said: (Feb 10, 2012)  
ok mr.gitty take 'x' only. u will get 4:5

=>1st number :2nd number

=> 20% more than X : 50% more than X

=> now cancel "more than X" on both sides

=> 20% : 50 %

=> 1.2 : 1.5

=> 4:5

Prashant said: (Feb 21, 2012)  
20% of 'x' + 'x' (20% more than third number)
=> 120/100x

Yash said: (Jun 23, 2012)  
I understand the method but why we add 100 in 20% and 50%. If we take third no is x so how a variable is added in 20% and 50%. But satish your method is simple and understood to me.

Bharadwaj said: (Aug 21, 2012)  
Sathish ratnam was explained very well.

Neethukasi said: (Sep 18, 2012)  
Ya ramesh's method is more easy.

Sajal Das said: (Oct 15, 2012)  
Let the 2 Nos are A and B and the 3rd No. is C.

According to the question A is 20% more than C. i.e., A=(1.2)C and B is 50% more than C. i.e., B=(1.5)C.

And so the ratio is {(1.2)C}/{(1.5)C} = 4/5 , i.e., 4:5.

Ramaniah said: (Nov 26, 2012)  
Let us know the number is x.

Then 1st number is 1.2x.

Then the 2nd number is 1.5x.

The the ratio of two numbers are 1.2x:15x=> 1.2 :1.5 =>4:5.

Hussain Ali said: (Jul 13, 2013)  
Let A, B, C are three numbers.

A is 20% more than C.

So A become:

A= C+20%of C = C+0.2C = 1.2C.

B become:
B= C+50%of(C)= C+0.5C = 1.5C.

And ratio between A/B is:
1.2C/1.5C = 4/5.

Hence answer is:4/5.

Hassan said: (Jul 18, 2013)  
Suppose a number,

100____120.

100 ___150.

Hence the numbers are increasing by 20 and 50%

120 : 150.

12 : 15.

4 : 5.

Nive said: (Aug 9, 2013)  
We know there are 3 numbers.

Think.,
1st one X.
2nd one Y.
3rd one Z.

Then assume that Z's value a.

Now X=a+20%.
Y=a+50%.

Put a=10.

Now we get X=12; Y=15.

So the ratio of X and Y is 4:5.

Nishant Raj said: (Sep 18, 2013)  
Very simple method is:

Let assume that 3th number is = 100.

Then,

a/c to ques. A = 120.

B = 150.

Ratio of number A/B = 120/150.

= 4/5.

A:B = 4:5 (ANS. C).

Naman said: (Nov 4, 2013)  
Ratio is 1.2 : 1.5 : 1.

= 12 : 15 : 10.

= 4 : 5 : 1.

Hence 4 : 5.

Gok said: (Nov 28, 2013)  
Please clearly say why you added 100 in 20% and 50%?

Giri said: (Jan 7, 2014)  
Let x be 3rd number then,

1st number is 20% greater than 3rd number,so 1st number is equal to

x+(x*(20/100)).
x(1+(20/100)).
x((100+20)/100).
x*(120/100).

That why we will add 100 to given percentage to find increase in it.

Mayank Mathur said: (Jan 18, 2014)  
Given % is 20 & 50.
Let the 3rd no is 100.

Then for A = 20% more means number is 120.
Similarly for B number is 150.

Ratio 120: 150.
12:15.
4:5 (divide by 3 to both number ).

Gaurav said: (Mar 30, 2014)  
Confused guys. Please read the question carefully.

Its first and 2nd number is 20% and 50 % more than the third number.

Obviously that means that the third number should be 100% or you can take it as 100.

Narayana Rao Gartam said: (Aug 7, 2014)  
Consider third number as 100, to do easy and better calculations.

Samira said: (Aug 9, 2014)  
Hey @Satish how you get 1.2 & 1.5 ?

Hemant said: (Sep 6, 2014)  
100+20:100+50 = 120:150 = 4:5.

Kavinraj said: (Sep 8, 2014)  
Hi.
my explanation is, assume your 3rd num is 10,

20%of 10=2 so 1st no is 12.
50%of 10=5, so 2nd no is 15.

So ratio of 12:15 = 4:5.

Svs said: (Oct 27, 2014)  
Hi, I really confuse.
Please clear my doubt.

Which is correct answer? Please tell.
@Sathya said 2:5.

Anyone tell correct answer?

Akshay said: (Oct 28, 2014)  
@Nive.

Method is actually according to the question approach. Its is valid.

a = c+20%.

b = c+50%.

a/b = 100c+20/100c+50.

Now c definitely having some value so consider it as 1 we can't consider it as 0 because it has some value and on other hand we have to consider it as 1 because it has some non zero value.

So a/b = 0.8 i.e. 4/5.

Rosh said: (Jan 16, 2015)  
Let 3rd no be x then.

(x+120/100):(x+150/100).

Take LCM 100 gets cancelled.

100x+120 = 100x+150.

We get 120 = 150.

So 4 : 5.

Abhinav said: (Feb 11, 2015)  
Let number = x, y, z.

Then, x = 20% of z + z = 6z/5.

y = 50% of z + z = 3z/2.

Ratio is x/y = 4/5.

B.Lingaswamyyadav said: (Mar 7, 2015)  
Let the third number will taken as 100.

= 120/100 = 150/100 = 12 = 15.

= 4 = 5.

Niz said: (Apr 1, 2015)  
If a, b, c.

a = c + 20% of c.

i.e a = c + 20/100*c.

a = c + 0.2 c.

i.e 1.2 c.

Also b = c + 50% of c.

i.e b = c + 50/100*c b = c + 0.5 c.

i.e 1.5 c.

Ratio between three numbers.

= 1.2 c : 1.5 c : c.

= 1.2 : 1.5.

i.e 4 : 5.

Jaity said: (Apr 30, 2015)  
But why did we took 120% instead of 20% and 150% in place of 50%?

Anish Sharma said: (May 18, 2015)  
Listen 20% more than third no and 50% more than through number.

So, First-> solve the 20% = 20/100 = 0.2.

But 20% more than third no, so we will add a third no.

And assume the third no. is x and x mean (1x) not a simple x.

So 0.2+1x = 1.2.

Second-> same for 50% = 50/100 = 0.5.

0.5+1x = 1.5.
= 1.2:1.5.
= 12:15.

So you can say: 4:5.

Santosh said: (May 31, 2015)  
Somebody let me know What is the ratio and what is the implementation of this?

Parikshit said: (Jun 30, 2015)  
Question says that two numbers are 20% and 50% MORE THAN third no then it should be like this:

No third no = X.

No A = 120*X/100+X.

B = 150*X/100+X.

But it gives 22:25.

Usha said: (Aug 14, 2015)  
Hey anyone can explain what is meaning by third number and how its became 20% to convert 120 and 150 please explain guys.

Vamshi said: (Sep 11, 2015)  
Let the third number be x = 100.

The first number is 20% more than third number so 100+20% = 120.

The second number is 50% more than third number so 100+50% = 150.

= 120:150 = 4:5.

Manas said: (Oct 3, 2015)  
Out of three number, the first number and the second number are respectively 25% and 30% less then the third number. By what percentage is the second number less then the first?

Can any one solve the problem? Then please.

Chex said: (Oct 9, 2015)  
Let x be the third value, hence.

20% of x = x+(20/100*x) = x+(x/5) = 6x/5.

50% of x = x+(50/100*x) = x+(x/2) = 3x/2.

Now ration is,

(6x/5)/(3x/2) = 12x/15x = 4/5.

Lokesh Anand said: (Oct 21, 2015)  
Let third number is 100.

Than 20% of third = 20 & 50% of third 50.

Than first number = 120(100+20).

Then second number = 150(100+50).

By question, Ratio of two number = First number:Second number.

= 120:150 = 4:5.

Ramanan said: (Nov 14, 2015)  
Let the third number be x given that:

x+20% : x+50%.

x+0.2 : x+0.5.

(we know x is '1x').

So, 1x+0.2 : 1x+0.5.

= 1.2x : 1.5x.

(To remove decimal points we are multiply in both sides by 10).

= 1.2x*10 : 1.5x*10.

= 12x : 15x.

By simplifying,

= 4 : 5.

(x will get cancelled when 12x/15x).

Harshitta said: (Feb 13, 2016)  
How to calculate to 1.2 and 1.15? How to get answer 4 = 5? I can't understand.

Shafai Rizvi said: (May 7, 2016)  
@Harshitta.

It is 1.2 and 1.5 (not 1.15).

So now simplify it,
= 1.2/1.5 (points cancel out).
= 12/15 (cancel out by 3).
= 4/5.

Maha said: (Jun 5, 2016)  
Lets us take c value as 100 then a value is 20% more.
So, c becomes 120
Similarly, b becomes 150 then, 120 : 150 becomes 4:5.

Sameer Khan said: (Jul 18, 2016)  
Ganapathy and Ramesh concept are easy and right.

Manish Kumar said: (Jul 26, 2016)  
What to do, if asked for third number?

Dibya said: (Aug 1, 2016)  
Sathi concept is good.

Manishanaveen said: (Aug 23, 2016)  
The third number be x.
Let a and b are two numbers with more than 20% and 50% of x.

a = x + 20%x.
b = x + 50%x.

We should find ratio a : b.

a/b = (x + 20%x)/(x + 50%x) we know % converted into (/100),
a/b = (x + 20x/100)/(x + 50x/100),
so we get a/b = (100x + 20X/100x + 50x).

a/b = (120x/150x)
a/b = 4/5.

Ratio of a = 4 and b = 5.

Shortcut: So just us 100 as x for removing %
a =100 + 20.
b =100 + 50.

a : b = 120 : 150.
And hence a/b = 12/15.
a/b = 4 : 5

Rakesh said: (Sep 7, 2016)  
@Ganapathy concept is very nice.

Anjaney said: (Sep 8, 2016)  
@Kunal.

It is 100 because ratio should be treated as 100.

Shahjahan said: (Oct 1, 2016)  
How you get 120 and 150? Confused. Please help me.

Cik_Nani said: (Oct 7, 2016)  
How do you get 120/100? And how do you get the answer 6 over 5? I'm confused. Please clarify me.

Abinash said: (Oct 20, 2016)  
If a and b incomes are in the ratio 9:4. Their expenditure are 8:3. Each saves rs 2500. Then expenditure of b?

Please tell me the answer for this.

Rashid Ali said: (Nov 28, 2016)  
The correct answer is 2:5.

I'm explaining bellow 20% means X is multiplied with 100.
For example : 95% of 80 = 80 * 95/100 = 76.
If you are agree with this concept then,

20% = 20/100 and 50/100.
20% = 1/5 and 50% = 1/2
A 1/5 : B 1/2 =2 : 5.

Hence answer is 2 : 5.

Rajini said: (Dec 22, 2016)  
Your concepts is good @Ganapathy and @Ramesh.

Alexa said: (Jan 13, 2017)  
% always means 100 so we 1st take 100 as the cmplt no.

Changaganjeet Singh said: (Mar 4, 2017)  
Your method is easy.

Thanks @Ramesh.

Chan Gaganjeet Singh said: (Mar 4, 2017)  
Let the third no. Be = 100.
Then add 100 in 20% and 50%.
It will be 120 and 150.
=120 : 150,
= 12 : 15,
= 4 : 5.

Shah Saain said: (Mar 18, 2017)  
@Ali.

Good and clear method. Thanks.

Aayusha said: (Apr 20, 2017)  
I understand now, thank @Satish Rathnam.

Juke said: (Apr 22, 2017)  
Here is my solution.

Let,
x be the first num.
y be the 2nd.
z be the 3rd.

x is larger than z by 20% so,
x=1.2z : z=x/1.2.
y is larger than z by 50% so.
y = 1.5z : z = y/1.5.
Equate z,
x/1.2 = y/1.5.
x/y = 1.2/1.5.
x/y = 4/5.

4:5.

Valar Morghulis said: (Jul 19, 2017)  
I have a doubt that most people are facing here it seems:

It's written 20% more than the third number so we took Z(third number) + (20/100)*Z.
What should be written if the equation comes as Z + 20/100?
Please, someone, take a time to help me and clarify this.
Thank you.

Ravi said: (Aug 18, 2017)  
Simply, we all know that in Case Of percent 100 % is max percentage.

So take 3rd number be 100%
A say more than 3rd no. That is 20%+100%=120% or 1.2
B say more than 3rd no. That is 50%+100%=150% or 1.5
Now, divide A/B=1.2/1.5=4:5.

Aafaque Ali said: (Nov 17, 2017)  
Percent = cent means 100 okey then.
20% n 50% just add them a 100.
120 n 150.
120 : 150 simplify.
4:5 Answer simple way.

Bdyachan said: (Dec 27, 2017)  
Let 3rd no. X.
20% of X =x/5,
So required no= X+x/5 =6x/5 (due to 20%more),
and 50% 0f X=x/2 , so required no =X+x/2=3x/2 (due to 50% more),
Now ratio =6x/5*2/3x=4:5 (ans 0).

Limsss said: (Sep 16, 2018)  
Thanks all for explaining this.

Azan said: (Oct 15, 2018)  
How come 120 and 150?

Riddhi said: (Nov 9, 2018)  
Why you take 100 here? Please explain me.

Sayani said: (Dec 14, 2018)  
We can assume the third number as 100.

Trimu said: (Dec 17, 2018)  
Let, The 3rd number be 100.

Then the 1st number is more than 20% than the 3rd number so 100+20=120.
Similarly, 2nd number is 100+50= 150.
Now the ratio of two numbers,
120:150,
4:5.

Anomie said: (Feb 2, 2019)  
@All who have a doubt that why does 100 only comes in place of x.

It is so because percentage is always 100. Therefore x = 100.

Sushant Pal said: (Mar 29, 2019)  
a : b:

20%:50%
20/100 = 2/5
50/100 = 1/2
a:b :: c:d.
2:5 :: 1:2.
= answer 5:4 or 5/4.

Bindu D K said: (Jul 13, 2019)  
20%= 120.
50% = 150.
120:150 = 120/150 = 4:5.

Sindhu said: (Jul 18, 2019)  
Let the third number be 100.
Then 20% of 100 is 20,
And 50% of 100 is 50,
Then the 1st number is 120,
The 2nd number is 150,
So, the ratio between 120 and 150 is 4:5.

Thanks.

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