Question

The average ago of doctors and lawyers together is 40.if the doctors average age is 35 and the lawyers age is 50,fine the ratio of the number of doctors to the number of lawyers​

Answer 1

Assumption

Number of doctors

= p

Also,

Number of lawyers

= n

According to Situation we have,

$\frac{Sum\;of\:p\:age\:of\:Doctor}{p} = 35$

(Sum of p age of doctor) = 35p

Again we have,

$\frac{Sum\:of\:n\:age\:of\:doctor}{y} =50$

Sum of n age of lawyer = 50n

Now,

$\frac{35p+50n}{p+n}=40$

35p + 50n = 40(p + n)

35p + 50n = 40p + 40n

50n - 40n = 40p - 35p

10n = 5p

2n = 1p

Now calculating the ratio we have :-

$\frac{2}{1}=\frac{p}{n}$

Hence,

The Required Ratio :-

p : n = 2 : 1

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Question :}}}}}$

The average age of doctors and lawyers together is 40.if the doctors average age is 35 and the lawyers age is 50,fine the ratio of the number of doctors to the number of lawyers.

________________________

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

let Number of doctors be x and number of lawyers be y

As we know formula for Average age :

$\small{\underline{\boxed{\sf{Average \: Age \: of \: Lawyers \: = \: \dfrac{Sum \: of \: Age \: lawyers}{Number \: of \: lawyers}}}}}$

Put these values

⇒50 = Sum of age/y

⇒Sum of age = 50y

∴ Sum of age of Lawyers is 50 y

________________________________

And for Doctors :

$\small{\underline{\boxed{\sf{Average \: Age \: of \: Doctors \: = \: \dfrac{Sum \: of \: Age \: doctors}{Number \: of \: doctors }}}}}$

Put values

⇒35 = Sum of age/y

⇒Sum of age = 35y

∴ Sum of age of Doctors is 35y

________________________________

And similarly for Average age of doctors and lawyers we have to add both the sum and number.

$\small{\underline{\boxed{\sf{Average \: Age \: = \: \dfrac{Sum \: of \: ages \: of \: Doctor \: and \: lawyers}{Number \: Doctor \: and \: lawyers}}}}}$

Put values

⇒40 = 50x + 35y/x + y

⇒40x + 40y = 50x + 35y

⇒40x - 50x = 35y - 40y

⇒-10x = -5y

⇒10x = 5y

⇒2x = 1y

⇒x/y = 2/1

So, the ratio of ages of Doctors and lawyers is 2:1

$\huge \implies {\boxed{\boxed{\sf{Ratio \: = \: 2:1}}}}$