At a certain party ratio the ratio of gents and ladies was 1:2 . But when 2…
2023
At a certain party ratio the ratio of gents and ladies was 1:2 . But when 2 gents and 2 ladies left the party . The ratio became 1:3. How many people were initially present in the party?
- A.
12
- B.
15
- C.
18
- D.
24
Attempted by 75 students.
Show answer & explanation
Correct answer: A
Solution:
Let the number of gents be x, so the number of ladies is 2x (given ratio 1:2).
After 2 gents and 2 ladies leave, the counts are x-2 and 2x-2 respectively. The new ratio is given as 1:3, so (x-2)/(2x-2) = 1/3.
Solve the equation: 3(x - 2) = 1(2x - 2) ⇒ 3x - 6 = 2x - 2 ⇒ x = 4.
Thus gents = 4 and ladies = 2x = 8. Total people initially = 4 + 8 = 12.