Question 14 Marks

Sunder is a fruit seller. Today he bought plums to sell. He purchased them at the rate of 9 for 100 from the wholesale market.
Q.1. How many plums should he sell for ₹40 if he wishes to gain 20%?
(a) 3$\quad$ (b) 4$\quad$(c) 5$\quad$(d) 8
Q.2.  He found that another fruit seller Kishan was selling plums at the rate of 6 for ₹90. Find the gain per cent of Kishan. (Assume that the wholesale rate is the same for all fruit sellers.
(a) 15%$\quad$(b) 20%$\quad$(c) 25%$\quad$(d) 35%
Q.3. Sunder decided to sell his plums at the rate of 7 for₹ 100. Find his gain per cent.
(a) $15 \frac{5}{9} \%$$\quad$(b) $17 \frac{7}{9} \%$$\quad$(c) $21 \frac{1}{9} \%$$\quad$(d) $22 \frac{2}{9} \%$
Q.4. In a box of 180 plums, he found that 28 were rotten and he had to throw them away. He sold the remaining plums at the rate of 8 for 100. Find his gain or loss per cent on this box.
(a) 2% gain$\quad$(b) 5% gain$\quad$(c) 2% loss$\quad$(d) 5% loss

Answer

1. (a): CP of 9 plums $=₹ 100$
If gain $\%=20 \%$ then SP of 9 plums $=₹\left(\frac{100+20}{100} \times 100\right)=₹\left(\frac{120}{100} \times 100\right)=₹ 120$.
$\therefore$ the number of plums for $₹ 40=\left(\frac{9}{120} \times 40\right)$ plums $=3$ plums.
$\therefore$ he should sell 3 plums for $₹ 40$ in order to gain $20 \%$.
2.
(d): For Kishan: CP of 9 plums $=₹ 100$ and SP of 6 plums $=₹ 90$.
$
\begin{array}{l}
\therefore \text { SP of } 9 \text { plums }=₹\left(\frac{90}{6} \times 9\right)=₹ 135 . \\
\text { Gain }=₹(135-100)=₹ 35 . \quad \text { [for } 9 \text { plums] } \\
\text { Gain } \%=\left(\frac{\text { gain }}{C P} \times 100\right) \%=\left(\frac{35}{100} \times 100\right) \%=35 \% .
\end{array}
$
3. (d): For Sunder: CP of 9 plums $=₹ 100$ and SP of 7 plums $=₹ 100$.
$
\begin{array}{l}
\therefore \text { SP of } 9 \text { plums }=₹\left(\frac{100}{7} \times 9\right)=₹\left(\frac{900}{7}\right) . \\
\text { Gain }=SP-CP=₹\left(\frac{900}{7}-100\right)=₹\left(\frac{200}{7}\right) . \\
\text { Gain } \%=\left(\frac{\text { gain }}{CP} \times 100\right) \%=\left\{\frac{\left(\frac{200}{7}\right)}{\left(\frac{900}{7}\right)} \times 100\right\} \%=\left(\frac{200}{900} \times 100\right) \%=\left(\frac{200}{9}\right) \%=22 \frac{2}{9} \% .
\end{array}
$
4. $( d ): CP$ of 9 plums $=₹ 100$
$
\therefore \quad \text { CP of } 180 \text { plums }=₹\left(\frac{100}{9} \times 180\right)=₹ 2000
$
Now, out of 180 plums, 28 were rotten.
$\therefore(180-28)=152$ plums were sold.
SP of 8 plums = ₹ 100 .
$
\therefore \text { SP of } 152 \text { plums }=₹\left(\frac{100}{8} \times 152\right)=₹ 1900
$
Thus, CP of that box of plum $=₹ 2000$ and $SP =₹ 1900$.
$
\begin{array}{l}
\therefore \text { loss }=CP-SP=₹(2000-1900)=₹ 100 \\
\text { Loss } \%=\left(\frac{\text { loss }}{CP} \times 100\right) \%=\left(\frac{100}{2000} \times 100\right) \%=5 \%
\end{array}
$

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