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### Question

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 6, 2 and 8 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

**A**

${3/19}$.

**B**

$1{2/9}$.

**C**

${1/7}$.

**D**

$2{6/7}$.

**Soln.**

**Ans: a**

Let the time taken by them to independently fill the tank be r, g and b minutes. Ink discharged by the blue tap is $3/b$. The total of all the inks is $3/r + 3/g + 3/b$. The ratio is ${1/b}/{1/r + 1/g + 1/b}$, which simplifies to ${rg}/{rg + gb + br}$ = ${3/19}$.