Question

Vijay has two types of soda bottles, divided in the ratio of 3:5. If 9 sodas bottles are finished from each type, then the ratio of the remaining soda bottles will be in the ratio 12:23. Find the total number of soda bottles initially.​

Answer 1

Given,

The initial ratio of the two types of soda bottles = 3:5

9 bottles are finished.

Final ratio becomes = 12:23

To find,

The initial numbers of soda bottles.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the initial numbers of two types of soda bottles = 3x and 5x (x is a variable)

Remaining soda bottles,

First type = 3x - 9

Second type = 5x - 9

According to the data mentioned in the question,

(3x-9)/(5x-9) = 12/23

69x-207 = 60x-108

69x-60x = 207-108

9x = 99

x = 11

Initially the number of,

First type of bottles = 3×11 = 33

Second types of bottles = 5×11 = 55

Hence, initially the number of two types of bottles were 33 and 55