1. ## Ratio

Ratio of two sums of money is 4:3

if larger sum of money is increased by $40, the ratio becomes 2:1. What are sums of money ? How to solve this ? Solution (4/7)*x+(3/7)*y=4:3 cant understand it.... 2. ## Re: Ratio Originally Posted by haftakhan Ratio of two sums of money is 4:3 if larger sum of money is increased by$40, the ratio becomes 2:1.

What are sums of money ?

How to solve this ?

Solution

(4/7)*x+(3/7)*y=4:3

cant understand it....
Dear haftakhan,

Let x and y be the sums of money. Take x as the larger sum.

$\displaystyle \frac{x}{y}=\frac{4}{3}$

If larger sum of money is increased by $40, the ratio becomes 2:1. Therefore,$\displaystyle \frac{x+40}{y}=2$Solve these two equations and find x and y. 3. ## Re: Ratio solving this i get x=160 and y=120 is it correct ? 4. ## Re: Ratio Originally Posted by haftakhan solving this i get x=160 and y=120 is it correct ? No. It is incorrect. 5. ## Re: Ratio$\displaystyle \frac{160}{120}= \frac{40(4)}{40(3)}= \frac{4}{3}$so those are in ratio 4:3. But adding$40 to $160 give$200.
$\displaystyle \frac{200}{12}= \frac{40(5)}{40(3)}= \frac{5}{3}$, or 5:3, not 2:1.

6. ## Re: Ratio

it may be easier to solve the two equations writing them like this:

3x = 4y
x+40 = 2y

one way of doing this, is to write (from the 2nd equation):

x = 2y - 40.

now use this in the first equation.

7. ## Re: Ratio

i was about to post the correct answer but the light went off.

x=80 and y=60

8. ## Re: Ratio

Originally Posted by haftakhan
i was about to post the correct answer but the light went off.

x=80 and y=60
Post #5 shows you how to check this answer for yourself.

9. ## Re: Ratio problem

ratio of two sums = 4 : 3 = $\displaystyle \frac{4}{3} = \frac{4x}{3x}$ ........... (1)
When $40 is increased to the larger sum, the ratio is =$\displaystyle \frac{4x+40}{3x} = \frac{2}{1}$.........(given)$\displaystyle \therefore 1\times (4x+40) = 2\times{3x}$=$\displaystyle 4x + 40 = 6x$=$\displaystyle 40 = 6x-4x$=$\displaystyle 2x = 40 $=$\displaystyle \therefore x = 20$By replacing the value of x in the first equation, we get$80 and $60. So the sum of$80 and $60 =$140.