The length and breadth of a rectangular tank are such that when each is increased by 6 m, their ratio becomes 7 : 5. When each is decreased by 8 m, their ratio becomes 1 : 3. Find the breadth of the tank.
2.75 meters
Let the length be L m and the breadth be B m.
First condition: \( \frac{L+6}{B+6}=\frac{7}{5}\Rightarrow 5L+30=7B+42\Rightarrow 5L=7B+12 \).
Second condition: \( \frac{L-8}{B-8}=\frac{1}{3}\Rightarrow 3L-24=B-8\Rightarrow B=3L-16 \).
Substituting: \( 5L=7(3L-16)+12=21L-100\Rightarrow 16L=100\Rightarrow L=6.25 \).
Then \( B=3(6.25)-16=18.75-16=2.75 \).
Hence, the breadth of the tank is 2.75 meters.
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