If two numbers are respectively 25% and 40% less than the third number what is the ratio numbers

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Given:

1st number = 25% less than 3rd number

2nd number = 45% less than by 3rd number

Formula used:

Percentage increment = increment/initial value × 100

If a quantity (x) is increased or decreased by a%, then

Final value of the quantity = (100 ± a)% of x,

Where ± shows the increment/decrement

Calculation:

Let, third number be X

1st number = (100 – 25)% of X

⇒ 75% of X

⇒ 0.75X

2nd number = (100 – 45)% of X

⇒ 55% of X

⇒ 0.55X

2nd number must be increased by = 0.75X – 0.55X

⇒ 0.2X

Percentage increment = (0.2X/0.55X) × 100

⇒ (0.2/0.55) × 100

⇒ 400/11%

⇒ 36.36%

∴ The percentage increment is 36.36%.

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Discussion :: Ratio and Proportion - General Questions (Q.No.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 X1.2. &2nd no will be X1.5. 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=20/100z+z y=50/100z +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 + 20/100c. a = c + 0.2 c. i.e 1.2 c. Also b = c + 50% of c. i.e b = c + 50/100c 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 = 120X/100+X. B = 150X/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+(20/100x) = x+(x/5) = 6x/5. 50% of x = x+(50/100x) = 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). = 1.2x10 : 1.5x10. = 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.

Aabir said: (Feb 5, 2020)
I could not understand it. Please explain it.

Prashant said: (May 15, 2020)
Why we convert this 20% to 120%?

Arya said: (Jun 12, 2020)
How you get to know that third number is 100? Please explain.

Ugyen Dema said: (Jul 21, 2020)
I am getting 2:5. Please anyone explain the answer clearly.

SHAIK MANSOOR said: (Oct 3, 2020)
They said comparing both 1st & 2nd third parts is less and it is Percentage. So For third part take it as 100%. Then for 1st part 120% & 2nd part 150%. Then 120% : 150% : 100%. Then the answers is 4:5.

Preetam Paul said: (Oct 11, 2020)
How come 120 percent? Please explain.

Ayushi said: (Jan 26, 2021)
Thanks @Ali.

Morepankh said: (Apr 8, 2021)
ATP, 1st no., Is 20% more than 3rd no. Let 3rd no., be x; Then, 1st no.,=(20/100)x+x. 2nd no.,=(50/100)x+x. Finally, 1st = 120x/100. 2nd = 150x/100. 3rd = x. Ratio required = 120x/100:150x/100. = 4:5.

N.PRASANTH said: (May 12, 2021)
120/100:150/100 = 120:150, = 12:15, = 4:5.

Shalini E said: (May 20, 2021)
Thank you all for explaining the concept.

Simran said: (May 22, 2021)
Let c is 1, then, first = 1 + 0.201, second = 1 + 0.501, ratio = 4:5.

Sravan said: (Aug 3, 2021)
Here, Why should we consider 100? Please explain.

Surya said: (Aug 20, 2021)
Thanks for explaining @Ganapathy.

Shakti said: (Sep 16, 2021)
Let 3rd number is "c" and the 1st and 2nd is; A,B. Then, A is the 20% more than c. Means A = c+20%c. = c+.2c. = 1.2c. Same hear, B is the 50% more than of c. Means. B = c + 50%c. = c + .5c, = 1.5c. Then the 2 number ratio is, A:B = 1.2c:1.5c. (Multiply in both sides 10 to avoid the decimal point) 1.2c * 10:1.5c * 10. 12c:15c, 4:5.

Samm said: (Sep 30, 2021)
How to solve if we have been asked the 2nd number is greater than 100. Like, Two numbers are respectively 40% and 110% more than a third number. The ratio of the two numbers is:? Anyone, please help me.

Divya said: (Dec 28, 2021)
@All. Here, First and second numbers 20% and 50% more that means 120:150 simply this we will get 4:5.

Rahul Kumawat said: (Aug 16, 2022)
Suppose the 3rd number is x. Then first no. will be more than 20% of third no. So first no.=x+20x/100=6x/5. second n0.=x+50x/100=3x/2. so, the ratio of first and second no.=6x/5*2/3x=4:5.