Aptitude - Ratio and Proportion - Discussion

Discussion :: Ratio and Proportion - General Questions (Q.No.10)

10. 

If Rs. 782 be divided into three parts, proportional to : : , then the first part is:

[A]. Rs. 182
[B]. Rs. 190
[C]. Rs. 196
[D]. Rs. 204

Answer: Option D

Explanation:

Given ratio = : : = 6 : 8 : 9.

1st part = Rs. 782 x 6 = Rs. 204
23


Green Violet said: (Jun 5, 2010)  
In wat way the ratio 1/2 : 2/3 : 3/4 is written as 6:8:9 ?

Answer Me said: (Jun 23, 2010)  
How did 6/23 come? Can anyone please explain?

Satish said: (Jun 24, 2010)  
Multiply 1/2 with 6, 2/3 with 4 and 3/4 with 3 so that numerator is same i.e. 12, hence 6:8:9

First part is 6 upon sum of 6+8+9=23 i.e. 6/23

Shreenath said: (Aug 17, 2010)  
How 1/2 is attained as 6 2/3 as 8 and 3/4 as 9 and how for calculating the first part the number is multiplied by 6/23 ?

Priya said: (Oct 12, 2010)  
The LCM of all the denominators is 12. So multiply the number and denominator with 6 to make 1/2 as 6/12, multiply 2/3 with 4. So that it becomes 8/12 and multiply 3/4 with 3 to make 9/12. Now the new ratio will be:

6/12, 8/12, 9/12.

Now cancelling 12 we will get 6, 8, 9.

Angel said: (Feb 2, 2011)  
You just need to multiply every ratio by 12 because it is the lcm of denominators.

Susant said: (Feb 3, 2011)  
@Priya

Thanks so much priya.

Sushil M said: (Apr 17, 2011)  
In wat way the ratio 1/2 : 2/3 : 3/4 is written as 6:8:9 ?

How's its come can u explain clearly ????

Kannan said: (Apr 26, 2011)  
Taking lcm for 2, 3, 4 and we got 12. Then the numerators 6, 8, 9 were used.

Hemant said: (May 8, 2011)  
1/2 : 2/3 : 3/4 is written as 6:8:9 ?
plz explain

Suman said: (Jun 9, 2011)  
1/2:2/3:3:4 is written as 6:8:9

how can you explain? plz explain clearly.

Shalu said: (Jun 14, 2011)  
1:2 is multiplyed by 6/6 then it will be 6/12,in second case 2:3 is multiplyed by 4/4 then 8/12, and 3:4 multyplyed by 3/3 then 9/12; it is done because of doing denominators equal,new ratio becomes 6:8:9.

Ranjani said: (Jul 5, 2011)  
Given :1/2:2/3:3/4=782

Let x b a part of 782 whn divided into 3 parts
(1/2)x:(2/3)x:(3/4)x=782

Take lcm we get
(6x+8x+9x)/12=782
23x=782*12
x=9384/23=408

Now we need 1 part so (1/2)*408 = 204.

Sanchit said: (Aug 6, 2011)  
Good ranjani. Your method is good :)

Raj said: (Aug 14, 2011)  
See their value is 1/2:2/3:3/4

Then take LCM 2,3,4 it's come 12

Then, (1/2:2/3:3/4)/12

Then 12/2=6 then 6*1=6
12/3=4 then 4*2=8
12/4=3 then 3*3=9

This way we find the 6:8:9.

Sushma said: (Aug 17, 2011)  
The given ratios are=1/2:2/3:3/4

Then take the LCM Of the denominator of ratios(2,3,4=12)

Then divide each ratio with 12. for eg:- 1/2*12=6.

Prapurna said: (Sep 20, 2011)  
I liked Ranjani's way of solving

Akash said: (Feb 27, 2012)  
Why we need sum of all the three? how did we know this in exam?

K Powar said: (May 25, 2012)  
This is a question on equivalent fraction. Since the ratio's are not equivalent, converting into equivalent fraction as under :

1/2 = 6/12
2/3 = 8/12
3/4 = 9/12

Hence, the ratio's are
6:8:9

or

6/23 ; 8/23; 9/23

First part : 782 * 6/23 = 204
Second part : 782 * 8/23 = 274
Third part : 782 * 9/23 = 306

Sharmila S. Meena said: (Jun 23, 2012)  
Priya explained very simply. I liked her method of solving.

Sravani said: (Aug 18, 2012)  
I liked Rajani's way of solving

T.Sathish Kumar said: (Jan 24, 2013)  
Easy method take 2, 3, 4 first divide by 2 then it becomes 1, 3, 2 then divide 2 then it becomes 1, 3, 1 then divide 3 it becomes 1, 1, 1 then take divided number 2*2*3=12 do like this my friend.

Chintamani said: (Feb 20, 2013)  
Why take LCM when we can directly simplify 1/2:2/3:3/4 by cancelling the common factor?

Deepa said: (Mar 27, 2013)  
Hi,

The given ratios are in fraction form that's why we have to convert the fraction form to whole number form with out changing the values of the ratios (only the form is changed and not the values) _. Then only the sum will b easy. And continue the sum as @K.POWAR said. I hope you can understand.

Kamal Bansal said: (Apr 26, 2013)  
Why we need sum of all the three? how did we know this in exam?

Rupam said: (Jun 8, 2013)  
Given Ratio = 1/2 : 2/3 : 3/4.

= 1/2*12 : 2/3*12 : 3/4*12.

= 6 : 8 : 9.

So 1st part is = Rs. (782 * 6/23) = Rs. 204.

[ to get 12.. do LCM of 2, 3 and 4 ].

Sanesh said: (Sep 3, 2013)  
I can't understand the 6/23 so please explain?

Kazi said: (Sep 8, 2013)  
Given that 1/2:2/3:3/4 = 782.

Let 782 divided in x parts.

Than (1/2x+2/3x)+3/4x = 782.

7x/6+3x/4 = 782.

46x/24 = 782.

x = 782*24/46.

x = 408.

1/2x = 1/2*408 = 204 1st no and so on.

Saikrish said: (Oct 9, 2013)  
(1/2+2/3+3/4)x = 782.

x = 408.

Then,

1/2 of x = 1/2*(408) = 204.

Dnyanesh said: (Feb 21, 2014)  
First We have to calculate LCM of 2,3,4. We get as 12.

Multiply each ratio i.e. numerator and denominator by 12 then we get ratio as 6:8:9.

Then calculate first part as {(782*6)/23} = 204 as answer.

Siddarth said: (Mar 26, 2014)  
Why is not 6:8:9/12 = 782 ?

I mean 782 must be multiplied by 12 so it should be 23x = 782*12.

Atul1487 said: (Apr 26, 2014)  
@Siddarth.

Because all values are in ratio not added or subtracted.
So 6/12:8/12:9/12 = 782.

Hence all 12s will be cancelled.
Hope you understood.

782 *12 will be happened only if,

6/12+8/12+9/12 = 782.
or
6/12-8/12-9/12 = 782.

Got it.

Sanjay Mishra said: (Jul 25, 2014)  
Only 782*6/23 where 23 is the sum of number.

Rohit said: (Aug 23, 2014)  
It is very simple methods. But it is not. Can solve apply to other method?

Monisha said: (Aug 29, 2014)  
Is there any other shortcut?

Anu said: (Sep 3, 2014)  
Let,
1/2x+2/3x+3/4x = 782.

Therefore solving x = 408.

From question, we need the first part, i.e. 1/2 of x = 204 :answer.

Siva J said: (Jun 3, 2015)  
Just simple calculation 1/2+2/3+3/4 = 23/12.

23/12 = 782.
1/2 = ?
782*1/2*12/23 = 204.

Sid said: (Jul 23, 2015)  
Thanks friends for helping in this.

Patel said: (Oct 24, 2015)  
1/2 = 50%.

2/3 = 66.67%.

3/4 = 75%.
____________

191.

982 x 50/191 = 204.

J K Reddy said: (Feb 21, 2016)  
Please anyone give me simple answer. I am not understand this methods how you will taken 12 please explain some body.

J K Reddy said: (Feb 23, 2016)  
Given 1/2, 2/3, 3/4.

The first part 1+2, 2+3, 3+4 (add).

3, 5, 7, the total : 15.

1/2*15 = 7.5.

2/3*15 = 10.

3/4*15 = 11.25.

This total : 28.75.

And 7.5/28.75*782 = 204.

We want first one so first one is 204.

So answer is 204.

Sonal said: (Mar 11, 2016)  
Given:- Amount = Rs. 782.

Ratios = 1/2:2/3:3/4.

Add the given ratios = 1/2+2/3+3/4 = 23/12.

To find the first part = given amount * first part ratio/total value of the ratios.

= 782*[ (1/2) / (3/4) ].

Answer = 204.

Akhila said: (Jun 20, 2016)  
Hi, I didn't get how 6/23 came, so plz explain it once again.

Rohan said: (Jun 23, 2016)  
Since the ratio is 6:8:9 = 23.

So, first part = 6/23,

Second part = 8/23,

Third part = 9/23,

We have to find the first part therefore 6/23.

Mohan Kumar said: (Jul 10, 2016)  
How 6:8:9?

Alen said: (Jul 17, 2016)  
You can it can also be done in this way divide the fractions like 1/2 = .5, 2/3 = .66 3/4 = .75 so the ratio would be like .5 : .66 : .75 .

This can be also written as 50 : 66 : 75.

According to some rule when all ratios in the given are multiplied with same number or value, the ratio or proportion remains the same.

Now, we can find the value of the first => 50/ 191 * 782 = 204.

Alam said: (Jul 20, 2016)  
At first to take lcm 2:3:4 then the result is 12.

Then after multiplying 1st part 1/2 * 12 = 6.

After multiplying 2nd part is 2/3 * 12= 8.
After multiplying 3rd part is 3/4 * 12 = 9.

The result is 6 : 8 : 9 after the result add it (6 + 8 + 9) = 23.

According to question find the 1st Part.

1st part is 6 and the total number is 23.

ie, 782 * 6/23 = 204 is the correct answer.

Ab Lakn said: (Sep 19, 2016)  
The answer will be 391 as the first part is half of 782.

Ajay said: (Oct 11, 2016)  
TAKE LCM(2,3,4) = 12;
THEN (6:8:9).

Tarun Dwivedi said: (Jan 23, 2017)  
Thank you @Angel.

Mujawar said: (Jan 31, 2017)  
Thanks for explaining the solution.

Karthivel said: (Feb 1, 2017)  
Not getting this.

Someone, please explain briefly.

S.Manikandan said: (Feb 21, 2017)  
Given data.

1/2 : 2/3 : 3/4 = 782.
=> (1/2)x:(2/3)x:(3/4)x = 782.
=> x/2 + 2x/3 + 3x/4 = 782.

L.C.M(2,3,4) = 12.
(6x+8x+9x)/12 = 782.
23x = 782 * 12.
x = 9384/23.
X = 408.

First part= (1/2) * 408 = 204.

Addu said: (Mar 8, 2017)  
Given ratio = : : = 6 : 8 : 9.

1st part = Rs. 782 x 6 = Rs. 204.

Sathyabama said: (Mar 19, 2017)  
I understand it easily, Thanks @Ranjani.

Srinivas said: (Apr 2, 2017)  
Given by 3 ratios into divided by some parts like 1/2 is the 1st part, 2/3 is the 2nd part,3/4 is the third part so,

We are talking 3 parts 1st we should follow L.C.M 2,3,4 = 12 so,
1/2 * 12 = 6(1st), 2/3 * 12 = 8(2nd), 3/4 * 12 = 9(3rd) then we adding those values 6 + 8 + 9 = 23 then now they are asking abt 1st part /total ratio*some money(Rs).
6/23 * 782 = 204.

So, the ans is [D].

Maruti said: (May 19, 2017)  
782 is divided into three parts A shares 1/2 which means half of 782.

I am Confused, please help me out.

Prashant said: (Aug 21, 2017)  
1st take the LCM of all denominators i.e 2,3,4 is 24 then multiply each ratio by 24. 1/2*24=12 , 2/3*24=16, 3/4*24=18.

Therefore ans is 12:16:18.
i.e 6:8:9. That's over

Johnny said: (Oct 11, 2017)  
I don't understand it, can someone explain?

Dennis said: (Nov 8, 2017)  
Simplify: (2x-4) - (6x+6).

Sup said: (Nov 22, 2017)  
Do LCM of 2,3,4.=12.

Now 1/2*12=6,2/3*12=8,3/4*12=9. That's 6:8:9.

Heer said: (Jan 3, 2018)  
I had rs 5000. I have to distribute between 3 people. In ratio 1:1/2:1/2. How did you divide it?

Sehrish Saleem said: (Jan 27, 2018)  
2500:1250:1250 Ans.
1+1/2+1/2= 1+0.5+0.5.
5000/2=2500.
1*2500=2500.
0.5*2500=1250.
0.5*2500=1250.
2500+1250+1250= 5000.

Nagu said: (Feb 6, 2018)  
1/2, 2/3, 3/4 how to calculate LCM? please explain.

S Gerald said: (Jul 12, 2018)  
1/2 of 782 is 391 right how it is 204?

Poornima said: (Jul 15, 2018)  
Hw to solve this (6/23)*782?

Prateek said: (Jul 23, 2018)  
Thanks so much @Priya.

Your answer was very useful to me.

Manisha Kumari said: (Aug 24, 2018)  
Thanks @Ranjani.

Nancy said: (Dec 7, 2018)  
Please explain this 1/2: 2/3: 3/4 =6 : 8 : 9.

Sathya said: (Dec 22, 2018)  
Take lcm of given ratio 1/2:2/3:3/4.
Lcm is 12.
So get 6:8:9,
Add 6, 8, 9 ans is 23,
So, 23 is 782 then 6 is 204.

Shashank Thakur said: (Jun 6, 2019)  
You can also solve it by adding all the ratio like:

1/2x+2/3x+3/4x = 782,
23x/12=782.
x = 408.

Hence for first part: 408*1/2= "204"=> answer.

Akila said: (Aug 10, 2019)  
How it would came 6:8:9?

Ramesh said: (Dec 12, 2019)  
Multiply all the ratio with LCM 12, then you get the answer.

Shoaib said: (Mar 6, 2020)  
Can somebody tell how to find LCM?

Jahangir Azhar said: (Apr 23, 2020)  
How did we get 408?

Arunkumar said: (Jul 26, 2020)  
Consider, Y = 1/2:2/3:3/4
X = 782.

In question they said proportional,
Then X proportional to Y.
Also, X=xY.
Then LCM for Y term is 12,
From solving we can find the value of x.
Then multiply the value of x with 1:2.

Varsha said: (Aug 15, 2020)  
How come 6 : 8 : 9? Please explain.

Prem said: (Sep 5, 2020)  
Well explained, Thanks @Priya.

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