Problem Solving

In a local theatrical production, the ratio of professional actors to amateur actors is 2:9. If the director were to hire two additional professionals and keep all amateurs in the cast, the ratio of professional to amateurs would be 1:4. How many total actors (professional and amateur) are in the cast of this production?

A) 11
B) 18
C) 21
D) 22
E) 33

Ans: D

Are you sure the ratio is 1:4 and not 1:3?

PLUG IN THE VALUES

i start from D (coincidence D is the OA )

P/A=2/9

now, P+A=22

P=(2/11)*22=4

A=18

NOW IF P IS ADDED WITH 2, THEN THE TOTAL WOULD BE 24 (PRO + ACT)
BUT THE THE amateur number i unchanged

that makes 6 profesianals and 18 amatuer

that makes the ratio 1:3

how do u know that P+ A = 22?

I think vishubn only makes a counter-example to show the ratio is wrong.

Yaaa, If the OA is 22 then no way the ratios is 1:4
pepeprepa was right ! i was countering it ! along

Vishu
cheers

Either the answer choices are wrong or the ratio is wrong.

If the ratio is right the answer is supposed to be 88.

Am I right guys

P = no of Profsnl Actors
A= no of amateur Actors

P/A = 2 /9

P=2x
A= 9x

(2x+2)/9x = 1/4

8x+8=9x
x=8

P=16
A=72

Total = P+A = 88