Question

There were an equal number of red balls and blue balls in a basket. After 20 red balls and 28 blue balls are removed from the basket, the ratio of the number of red balls to the number of blue balls becomes
5:3. Find the total number of red balls in the basket.
Please answer this question step by steps. ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

There were an equal number of red balls and blue balls in a basket. After 20 red balls and 28 blue balls are removed from the basket, the ratio of the number of red balls to the number of blue balls becomes 5:3

TO DETERMINE

The total number of red balls in the basket

EVALUATION

Let x be the total number of red balls in the basket

Then the total number of blue balls in the basket = x

After 20 red balls and 28 blue balls are removed from the basket

The remaining number of red balls in the basket

$= x - 20$

The remaining number of red balls in the basket

$= x - 28$

By the given condition

$\displaystyle \: (x - 20) : \: (x - 28) = 5 : 3$

$\displaystyle \: \frac{ (x - 20) }{(x - 28) } \: = \frac{5}{3}$

$\implies \: 5x - 140 = 3x - 60$

$\implies \: 2x = 80$

$\implies \: x = 40$

RESULT

$\sf \boxed{ \:The \: total \: number \: of \: red \: balls \: in \: the \: basket = 40 \: }$