Question

Rs 180 is to be divided among 66 persons (men and women). The ratio of the total amuont of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is

(a) 20 

(b) 24 

(c) 30 

(d) 36

Answer 1

(c) 30

Let the number of men be x. 

Then, number of women = 66 – x 

Money received by x men = \(\frac{5}{(5+4)}\) x Rs 180 = Rs 100 

∴ Money received by (66 – x) women = Rs (180 – 100) = Rs 80 

Given, \(\frac{100}{x}\) : \(\frac{80}{66-x}\) = 3 : 2

⇒ \(\frac{100}{x}\) x \(\frac{66-x}{80}\) = \(\frac32\) 

⇒ \(\frac{200}{x}\) = \(\frac{240}{66-x}\) ⇒ 240x = 13200 – 200x 

⇒ 440x = 13200 ⇒ x = \(\frac{13200}{440}\) = 30