Question

The ratio of number of ladies to gents at a party was 1:2, but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were originally present at the party?

I did like this
1x + 2x = y (I assumed y as total no. of people). [Equation 1]
1x + 3x = y-4 (Because 4 left in total). [Equation 2]
after solving I get x=-4
but a answer is 4

please experts help. Tell me where I am going wrong.

Answer 1

Hi,

Now I did understood by what method you're doing this but you've to think it different way.

So the ratio is 1:2 ladies to gents

Assume x is ladies and 2x is gents.

Now, 2 ladies and 2 gents left and now ratio is 1:3, so

:• (x - 2) / (2x - 2) = 1 / 3

:• (x - 2) / 2(x - 1) = 1 /3

:• 3(x - 2) = 2(x - 1)

:• 3x - 6 = 2x - 2

:• 3x - 2x = -2 + 6

:• x = 4

So there were 4 ladies and 8 gents and total number of people were 12.

THANK YOU