RS Aggarwal 2019,2020 solution class 7 chapter 11 Profit and Loss Test Paper 11

Test Paper 11

paper-160

Question 1:

By selling a chair for Rs 1375 a man gains 10%. Find its cost price.

Answer 1:

SP of the chair = Rs 1375
Gain% = 10

 $\mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{c}\mathrm{hair}=\{\frac{100}{(100 + \mathrm{Gain}\%)}\times \mathrm{SP}\}$

$$\begin{gathered} =\{\frac{100}{(100 + 10)}\times 1375\} \\ =\frac{137500}{110} \\ = \mathrm{Rs}. 1250 \end{gathered}$$

Question 2:

If the selling price of 10 pens is equal to the cost price of 14 pens, find gain per cent.

Answer 2:

Let the cost of each pen be Rs. 1
CP of 10 pens = Rs. 10
SP of 10 pens = CP of 14 pens = Rs. 14
Gain = SP - CP = 14-10= Rs. 4
$$\begin{gathered} \mathrm{Gain}\% = \left(\frac{\mathrm{Gain}}{\mathrm{CP}} \times 100\right)\% \\ = \left(\frac{4}{10}\times 100\right)\% \\ = 40\% \end{gathered}$$

Question 3:

On selling a fan for Rs 2585 a man gains $\frac{1}{10}$ of its cost price. Find the cost price of tha fan.

Answer 3:

Let the cost price of the fan be Rs. x.
Gain = $\mathrm{Rs}. \frac{x}{10}$
SP of the fan = $( x + \frac{x}{10})= \mathrm{Rs}. \frac{11}{10}x$                                                                  
SP of the fan = $\mathrm{Rs}. 2585$      
∴  $\frac{11}{10}x = 2585$
⇒ $11x = 25850$ 
⇒ $x = \frac{25850}{11} = 2350$


So, CP of the fan is Rs. 2350.

Question 4:

A man buys lemons at 6 for Rs 10 and sells at 8 for Rs 15. Find his gain per cent.

Answer 4:

Cost price of six lemons = Rs. 10
Cost price of one lemon = $\mathrm{Rs}. \frac{10}{6}$
Cost price of eight lemons =  $8 \times \frac{10}{6} = \mathrm{Rs}. \frac{80}{6} = \mathrm{Rs}. 13.33$                                         
Selling price of eight lemons = Rs. 15

  $$\begin{gathered} \mathrm{Gain\; =\; S}P-\; CP \\ =\mathrm{Rs}. (15 - 13.33) \\ = \mathrm{Rs}. 1.67 \end{gathered}$$ 
                                                           
Gain% = $\left(\frac{\mathrm{Gain}}{C.P.}\times 100 \right)$%
$=\left(\frac{1.67}{13.33}\times 100\right)$%
$=12.5$%

Question 5:

On selling a bat for Rs 486 a man loses 10%. Find the cost price of the bat.

Answer 5:

SP of the bat = Rs 486
Loss = 10%
CP of the bat = $\{\frac{100}{(100 - \mathrm{Loss}\%)}\times SP\}$
$$\begin{gathered} =\{\frac{100}{(100 - 10)}\times 486\} \\ = \frac{48600}{90} \\ = \mathrm{Rs} 540 \end{gathered}$$


CP of the bat = Rs 540

Question 6:

Mark (✓) against the correct answer
On selling a football for Rs 100, a man gains Rs 15. The cost price of the football is

(a) Rs 115
(b) Rs 85
(c) Rs 70
(d) Rs 130

Answer 6:

(b) Rs 85

SP of a football = Rs 100
Gain = Rs 15
Gain = SP - CP
        ⇒    15 = 100 - CP
       ⇒    CP = Rs (100 - 15)
       ⇒    CP= Rs 85

Question 7:

Mark (✓) against the correct answer
A vendor buys lemons at Rs 25 per dozen and sells at 5 for Rs 12. His gain per cent is

(a) 14.5%
(b) 15%
(c) 15.2%
(d) 16%

Answer 7:

(c) 15.2%

Cost price of 12 bananas = Rs. 25
Cost price of one banana = $\mathrm{Rs}. \frac{25}{12}$
  $$\begin{gathered} \mathrm{Cost} \mathrm{price} \mathrm{of} \mathrm{five} \mathrm{banana}s=\mathrm{Rs}. 5 \times \frac{25}{12} \\ = \mathrm{Rs}. \frac{125}{12} \\ =\mathrm{Rs}. 10.42 \end{gathered}$$                                                       

He sells five bananas at the cost (SP) of Rs. 12.
Gain = SP - CP

= $$\begin{gathered} =\mathrm{Rs}. (12 - 10.42) \\ = \mathrm{Rs}. 1.58 \end{gathered}$$     

 $$\begin{gathered} \mathrm{Gain}\% = \left(\frac{\mathrm{Gain}}{CP}\times 100\right)\% \\ = \left(\frac{1.58}{10.4}\times 100 \right)\% \\ = 15.2\% \end{gathered}$$                                    

Question 8:

Mark (✓) against the correct answer
On selling a jug for Rs 168, a man loses $\frac{1}{7}$ of his outlay. The cost price of the jug is

(a) Rs 144
(b) Rs 192
(c) Rs 196
(d) none of these

Answer 8:

(c) Rs. 196

Let the cost price of the jug be Rs. x.
Loss = $\mathrm{Rs}. \frac{x}{7}$
SP of the jug = CP - Loss
$$\begin{gathered} =\mathrm{Rs}. ( x - \frac{x}{7}) \\ = \mathrm{Rs}. \frac{6}{7}x \end{gathered}$$                                       
                                                                                    
​SP of the jug = $Rs 168$         (given)

∴   $\frac{6}{7}x = 168$
$$\begin{gathered} \Rightarrow =\frac{168 \times 7}{6} \\ \Rightarrow x= \frac{1176}{6} \\ \Rightarrow x=196 \end{gathered}$$                    
   
∴ CP of the jug = $\mathrm{Rs}. 196$

Question 9:

Mark (✓) against the correct answer
If the cost price of 5 bananas be equal to the selling price of 3 bananas, then gain per cent is

(a) $33\frac{1}{3}\%$
(b) 15%
(c) $66\frac{2}{3}\%$
(d) 40%

Answer 9:

(c) $66\frac{2}{3}\%$

Let the cost price of each banana be Re 1.
Cost price of three bananas = Rs. 3
SP of three bananas = CP of five bananas = Rs. 5
Gain = SP - CP =  $\mathrm{Rs}. ( 5 - 3 ) = \mathrm{Rs}. 2$     
                                                        
 $$\begin{gathered} \mathrm{Gain}\% = \left(\frac{\mathrm{Gain}}{CP}\times 100\right)\% \\ = \left(\frac{2}{3}\times 100\right)\% \\ =\left( \frac{200}{3}\right) \% \\ = 66\frac{2}{3}\% \end{gathered}$$
                                 

Question 10:

Fill in the blanks.

(i) Loss = (CP) − (......).
(ii) CP = $\frac{100\times \mathrm{SP}}{(......+......)}$.
(iii) Profit or loss is always reckoned on ...... .
(iv) $\frac{100}{(100-\mathrm{loss}\%)}\times \mathrm{SP}=...... .$

Answer 10:

(i) Loss = (CP) - (SP)

(ii) CP = $\frac{100 \times SP}{(\underline{\underline{100}} + \mathrm{Gain}\%)}$

(iii) Profit or loss is always reckoned on the cost price.
(iv)  $\frac{100 \times \mathrm{SP}}{(100 - \mathrm{loss}\%)}$ = CP

Question 11:

Write 'T' for true and 'F' for false

(i) Loss is reckoned on selling price.
(ii) Gain is reckoned on cost price.
(iii) $\mathrm{CP}=\frac{100\times \mathrm{SP}}{(100-\mathrm{loss}\%)}.$
(iv) Loss = (CP) − (SP).

Answer 11:

(i) False
Gain or loss is always reckoned on the cost price.
  
(ii) True
(iii) True
(iv) True