Question

The average age of consisting doctors and lawyers is 40. If the doctors average age is 35 years and the lawyers average age is 50 years, find the ratio of the number of doctors to the number of lawyers.

Answer 1

Step-by-step explanation:

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Answer 2

Given that,

• The average age of consisting doctors and lawyers is 40.

❍ Let's say, that the number of doctors be x and number of lawyers be y respectively.

Also,

• If the doctors average age is 35 years and the lawyers average age is 50 years.

Therefore,

➟ Sum of average age of doctors is 35x.

➟ Sum of average age of lawyers is 50y.

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As we know that,

$\bigstar\:\underline{\boxed{\frak{Average = \dfrac{Sum \;of\; Observation}{Total\; number\;of\; Observation}}}}$

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$:\implies\sf\dfrac{x_{age}+y_{age}}{x + y} \\\\\\:\implies\sf \dfrac{35x + 50y}{x+y} = 40 \\\\\\:\implies\sf 40(x + y) = 35x + 50y\\\\\\:\implies\sf 40x + 40y = 35x + 50y\\\\\\:\implies\sf 40x - 35x = 50y - 40y\\\\\\:\implies\sf 5x = 10y\\\\\\:\implies\sf \dfrac{x}{y} = \cancel\dfrac{10}{5} \\\\\\:\implies\sf \dfrac{x}{y} = \dfrac{2}{1}\\\\\\:\implies\underline{\boxed{\pmb{\frak{\pink{x : y = 2 : 1}}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence, the ratio of the number of doctors to the lawyers is \textbf{2 :1}.}}}$