A shopkeeper 7

A shopkeeper bought 80 cricket bats for 2.55 euros each. He sells 20 of them at a 5% gain. What must be the gain percentage of the remaining bats to get a 10% gain overall?

Correct answer:

g₂ =  11.6667 %

Step-by-step explanation:

$$\begin{gathered} n=80 \\ {r}_1=100\%+5\%=1+\frac{5}{100}=1.05 \\ {n}_1=20 \\ {n}_2=n-n_1=80-20=60 \\ r=100\%+10\%=1+\frac{10}{100}=1.1 \\ r\cdot n=n_1\cdot r_1+n_2\cdot r_2 \\ 1.1\cdot 80=20\cdot 1.05+60\cdot r_2 \\ 60r_2=67 \\ {r}_2=\frac{67}{60}=1.11666667 \\ {r}_2=\frac{67}{60}\doteq 1.116667 \\ {g}_2=100\cdot (r_2-1)=100\cdot (1.1167-1)=11.6667\% \end{gathered}$$

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