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

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

Answer: Option C

Explanation:

Let the third number be x.

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

Ans= 2:5 ?

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

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

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?

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....

=>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

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.

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.

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.

100____120.

100 ___150.

Hence the numbers are increasing by 20 and 50%

120 : 150.

12 : 15.

4 : 5.

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.

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).

= 12 : 15 : 10.

= 4 : 5 : 1.

Hence 4 : 5.

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.

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 ).

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.

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.

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

Anyone tell correct answer?

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.

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

Take LCM 100 gets cancelled.

100x+120 = 100x+150.

We get 120 = 150.

So 4 : 5.

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

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

Ratio is x/y = 4/5.

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

= 4 = 5.

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.

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.

No third no = X.

No A = 120*X/100+X.

B = 150*X/100+X.

But it gives 22:25.

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.

Can any one solve the problem? Then please.

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.

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.

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).

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.

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

It is 100 because ratio should be treated as 100.

Please tell me the answer for this.

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.

Thanks @Ramesh.

Good and clear method. Thanks.

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.

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.

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.

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.

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

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

Thanks.

Then for 1st part 120% & 2nd part 150%.
Then 120% : 150% : 100%. Then the answers is 4:5.

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.

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.

Like, Two numbers are respectively 40% and 110% more than a third number. The ratio of the two numbers is:?

Anyone, please help me.

Here,

First and second numbers 20% and 50% more that means 120:150 simply this we will get 4:5.

Ratio is ---- (c) 4 : 5.

So, Option (C) is the Right answer.