# Discussion of Question with ID = 031 under Pipes-and-Cisterns

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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 7, 3 and 6 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${7/27}\$.

B

\$1{4/13}\$.

C

\${7/29}\$.

D

\$3{1/29}\$.

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}\$ = \${7/27}\$.