Question

three equal glasses are filled with a mixture of spirit and water.

Answer 1

Option (B) - 401:544

Explanation:

Given that total number of glasses = 3.

Given That ratio of spirit and water in each glass is 2:3,3:4,4:5.

Amount of spirit in 1st glass = 2/(2 + 3)

                                               = 2/5.


Amount of Spirit in 2nd glass = 3/(3 + 4)

                                                  = 3/7.


Amount of spirit in 3rd glass = 4/(4 + 5)

                                                = 4/9.



Therefore total amount of spirit = 2/5 + 3/7 + 4/9

LCM of 5,7,9 = 315.

                                                      = 2 * 63 + 3 * 45 + 4 * 35/315

                                                      = 401/315.    ------- (1)

                                                      


Now,

The amount of water in 1st glass = 3/(2 + 3)
        
                                                        = 3/5.


The amount of water in 2nd glass = 4/(4 + 3)

                                                         = 4/7.


The amount of water in 3rd glass = 5/(5 + 4)

                                                         = 5/9.



Therefore the total amount of water = 3/5 + 4/7 + 5/9

LCM of 5,7,9 = 315.

                                                             = 3 * 63 + 4 * 45 + 5 * 35/(315)

                                                             = 544/315.    -------- (2)


From (1) & (2), we get

The required ratio = 401:544.

Hope this helps!

Answer 2

Given that,

The ratio of spirit and water in first glass = 2:3

The ratio of spirit and water in second glass = 3:4

The ratio of spirit and water in third glass = 4:5

We need to calculate the quantity of spirit

Using given data

$spirit=\dfrac{\text{quantity of spirit in first glass}}{\text{total mixture in first glass}}+\dfrac{\text{quantity of spirit in second glass}}{\text{total mixture in second glass}}+\dfrac{\text{quantity of spirit in third glass}}{\text{total mixture in third glass}}$Put the value into the formula

$spirit=\dfrac{2}{2+3}+\dfrac{3}{3+4}+\dfrac{4}{4+5}$

$spirit=\dfrac{401}{315}$

We need to calculate the quantity of water

Using given data

$water=\dfrac{\text{quantity of water in first glass}}{\text{total mixture in first glass}}+\dfrac{\text{quantity of water in second glass}}{\text{total mixture in second glass}}+\dfrac{\text{quantity of water in third glass}}{\text{total mixture in third glass}}$Put the value into the formula

$water=\dfrac{3}{2+3}+\dfrac{4}{3+4}+\dfrac{5}{4+5}$

$water=\dfrac{544}{315}$

We need to calculate the ratio of spirit and water in the resulting mixture

Using given data

$\dfrac{spriti}{water}=\dfrac{\text{quantity of spirit}}{\text{quantity of water}}$

Put the value into the formula

$\dfrac{spriti}{water}=\dfrac{401}{315}\times\dfrac{315}{544}$

$\dfrac{spriti}{water}=\dfrac{401}{544}$

Hence, The ratio of spirit and water in the resulting mixture is 401:544