Q5 of 33 Page 44

In a co-operative society, the number of men is thrice the number of women. 29 women and 16 men more joined the society and now the number of men is double the number of women. How many women were there in the society at first?


Lethe original number of women in the society be x.

Since number of men is thrice the number of women,


Number of men = 3x


Number of women after joining of 29 more women = x + 29


Number of men after joining of 16 more men = 3x + 16


Since, the new number of men is twice the number of women


∴ 3x + 16 = 2(x + 29)


Solving the brackets, we get


3x + 16 = 2x + 2 × 29


⇒ 3x + 16 = 2x + 58


⇒ 3x = 2x + 58-16


⇒ 3x = 2x + 42


⇒ 3x-2x = 42


⇒x = 42


Hence, number of women in the society at first = x = 42


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