# Aptitude - Ratio and Proportion - Discussion

Discussion Forum : Ratio and Proportion - General Questions (Q.No. 3)
3.
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Rs. 500
Rs. 1500
Rs. 2000
None of these
Explanation:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x - 3x = 1000

x = 1000.

B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Discussion:
72 comments Page 1 of 8.

JPE said:   4 months ago
Solution:

4x - 3x = 1000
x = 1000.

b -> 2x so, 2*1000 = 2000.

Explanation:
5:2:4:3 can be written as 5x + 2x + 4x + 3x = total amount shared between them.

(Hint -> whenever the answer required is in terms of an integer like find the amount, no. of students, no, of people, the amount spent or whatever it may be always represent the given ratio in terms of x).

so, 4x -> c, 3x -> d.

4x-3x = 1000(because if d gets 1000 , c will get 2000 or if d gets 100 c will get 1100 if u subtract their two amounts u should get 1000 as difference.)
4x-3x = 1000
x = 1000.
.
question -> Find B's share.
So, b is 2x
Then, 2*1000 = 2000.
(3)

Setor said:   5 years ago
@All.

According to me;
From the question; C gets 1000 more than D.
Hence C= 1000+D --> (1)
Now from the proportion given, A:B:C:D is equal to 5:2:4:3.
We can then say C:D = 4:3.
or C/D = 4/3 ---> (2)

Put equation (1) into (2)
4/3 = (1000 +D)/ D (using change of subject D= 3000).

Remember the unknown is B.
hence utilizing the proportion with the known values:
2:4 = B: C.
2/4 = B/(1000+3000) NB: c= 1000 +D from equation 1.

Thus using a change of subject B = 2000.

Hi,

This sum can be solved very simply without using paper and pen also. First read the question properly.

C is getting Rs 1000 more than D so C is having more money than D.

C is having 4x and D is having 3x, the difference between both is given as 1000. So 4x-3x=1000, x=1000. So C is having 4000.

How much money B is having ? B is having half of the money with C, because B is 2x. C is 4x so B =2000 (half of the money OF C).

@Ramesh

I guess your doubt has not been cleared properly. So, i'll give it a try. For example, if the money is divided between A and B in the ratio 3:5;
then, A:B=3:5.

We can also write; A/B=3/5 which means we can exchange B and 3 and rewrite as A/3=B/5. Then if A/3=B/5=x here x is a constant. Then we can write A=3x and B=5x right?

And a proportion is for example A:B=C:D which states that two ratios are equal.

Faizan said:   10 years ago
x is total money. Now, shares of A, B, C and D comes out to be 5x/14, 2x/14, 4x/14, and 3x/14. (5+2+4+3=14), Now Acc. to question, C is getting 1000 more than D.

Which means "[(4x/14)-(3x/14)]=1000" find x from here, which comes to be 14000. Now we can find B's share as (B=2x/14), put value of x, and B comes 2000.

In the same way we can find share of any one.

We can solve it by also the following method;
let the sum of the money be X.
then,5X/14+2X/14+4X/14+3X/14=X. [because(5+2+4+3=14)
A's share=5X/14,B's share=2X/14,C's share=4X/14 and D's share=3X/14
It is given that C gets Rs. 1000 more than D,
i.e, 4X/14=1000+3X/14
4X/14-3x/14=1000
X/14=1000
X=14000.
So, B's share is 2X/14=2*14000/14 = 2000 Rs.
(1)

The common term from both ratios is 'B'.

So the solution will be,

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

In 5 (A:B) , the value 5 corresponds to the value of B in second ratio.

Similarly, in 4 (B:C) , the value 4 corresponds to the value of B in the first ratio.

Thus, 5 (A:B) :4 (B:C) = 5 (3:4) :4 (5:6).

= (15:20) : (20:24).

= (15:20:24).

Let suppose total sum of money is 'X'.

And total of the proportion is 5+2+4+3 = 14.

So one unit of the proportion is X/14.

Then C gets X/14*4 and D gets X/14*3.

According to question C gets 1000 more than D.

So (X/14*4)-(X/14*3) = 1000 solving this we get.

X = 14000.

So, B's share is X/14*2.

= 14000/14*2 = 2000.

Ravi said:   7 years ago
@Deepa.

There are 4no.

A, B, C, D=5x, 2x, 4x, 3x (respectivly).

The Question says c get Rs 1000 more than D which means.

We have C as 4x. And D as 3x so.
4x=3x+1000. Ok (ques says).
Then 4x-3x=1000.
Therefore x=1000.

We have to find of B. Then B has 2x=>2*1000=2000 (x=1000).

JJA said:   10 months ago
Let the total sum of money be x.

5 + 2 + 4 + 3 = 14.

If C - D=1000.

Then:
4/14(x) - 3/14(x) = 1000,
[4/14 - 3/14]x = 1000.

Since the fractions have the same denominator, we can break it down as;

1/14 x = 1000,
x = 1000 * 14,
x= 14000.

If the ratio of B is 2/14.
2/14 * 14000 = 2000,
So, B = 2000.
(14)