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31
Abhishek purchased 140 shirts and 250 trousers @ Rs. 450 and @ Rs. 550 respectively. What should be the overall average selling price of shirts and trousers so that 40% profit is earned ? (rounded off to next integer)
Discuss
Answer & Solution
Answer: Option C
Solution:
Total Cost Price
= Rs. (140 × 450 + 250 × 550)
$$\eqalign{ & = {\text{Rs}}.\left( {63000 + 137500} \right) \cr & = {\text{Rs}}{\text{. }}200500. \cr & {\text{Total Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{140}}{{100}} \times 200500} \right) \cr & = {\text{Rs}}{\text{. }}280700. \cr & \therefore {\text{Average Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{140 + 250}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{390}}} \right) \cr & = {\text{Rs}}{\text{. }}719.74 \approx 720 \cr} $$
32
A man sells two chairs at Rs. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Rs. is = ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of first chair}} \cr & = \frac{{100}}{{125}} \times 120 = {\text{Rs}}{\text{.}}\,96 \cr & {\text{C}}{\text{.P}}{\text{.}}\,\,{\text{of}}\,{\text{second}}\,{\text{chair}} \cr & = \frac{{100}}{{75}} \times 120 = {\text{Rs}}{\text{.}}\,160 \cr & \therefore {\text{Loss}} = 160 + 96 - 240 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,16 \cr} $$
33
A man wanted to sell an article with 20% profit: but he actually sold at 20% loss for Rs. 480, at what price he wanted to sell it to earn the profit = ?
Discuss
Answer & Solution
Answer: Option A
Solution:
According to the question,
$$\eqalign{ & {\text{Loss }}20\% \cr & {\text{Selling price}} \cr & = 100\% - 20 = 80\% \cr & 80\% = 480 \cr & 1 = \frac{{480}}{{80}} \cr & \therefore \left( {{\text{Profit }}20\% } \right) \cr & = \frac{{480}}{{80}} \times 120 \cr & = {\text{Rs}}{\text{. }}720 \cr} $$
34
A shopkeeper sells an article at a loss of $$12\frac{1}{2}$$% . Had he sold it for Rs. 51.80 more, he would have earned a profit of 6% . The cost price of the article is = ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Let C.P. be Rs. x Then
(106% of x) - $$\left( {87\frac{1}{2}\% \,\,{\text{of}}\,x} \right) = 51.80$$
$$\eqalign{ & \Rightarrow 18\frac{1}{2}\% \,\,{\text{of}}x = 51.80 \cr & \Rightarrow x = \left( {\frac{{51.80 \times 100 \times 2}}{{37}}} \right) \cr & \therefore x = 280 \cr} $$
35
A person purchased 10 dozen pens at the rate of Rs. 4 per dozen. On checking, he found that 20 pens were not working. In order to earn 25% profit, he should sell the remaining pens each at -
Discuss
Answer & Solution
Answer: Option C
Solution:
Total C.P. of (10 × 12) i.e.,
120 pens = Rs. (4 × 10) = Rs. 40
Number of working pens
= (120 - 20) = 100
Total selling price of 100 pens
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times 40} \right) \cr & = {\text{Rs}}{\text{. }}50. \cr & \therefore {\text{S}}{\text{.P}}{\text{.of each pen}} \cr & = {\text{Rs}}.\left( {\frac{{50}}{{100}}} \right) \cr & = {\text{50 paise}}{\text{}} \cr} $$
36
Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20% ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Let the C.P. be Rs. }}x \cr & {\text{Then, }}20\% {\text{ of }}x = 1100 \cr & \Rightarrow \frac{{20}}{{100}} \times x = 1100 \cr & \Rightarrow x = 5500 \cr & {\text{C}}{\text{.P}}. = {\text{Rs}}{\text{. }}5500 \cr} $$
Expenditure on repairs = 10%
$$\eqalign{ & {\text{Actual price}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 5500} \right) \cr & = {\text{Rs}}{\text{. }}5000. \cr & \therefore {\text{Expenditure on repairs}} \cr & = {\text{Rs}}.\left( {5500 - 5000} \right) \cr & = {\text{Rs}}{\text{. }}500 \cr} $$
37
A person sells a table at a profit of 10% . If he had bought the table at 5% less cost and sold for Rs. 80 more, he would have gained 20% . The cost price of the table is = ?
Discuss
Answer & Solution
Answer: Option C
Solution:
Let the CP1 of Table = 100x
Initial SP1 = 100x + 10% of 100x = 100x + 10x = 110x
Now, If He brought table at 5% discount. Therefore CP2 = 95x
Now SP2 = 95x + 20% of 95x = 95x + 19x =114x
According to question
SP2 - SP1 = 80
⇒ 114x - 110x = 80
⇒ 4x = 80
⇒ x = 20
Initial Cost of table = 100 × 20 = Rs. 2000
38
A radio is sold for Rs. 990 at a profit of 10% . What would have been the actual profit or loss on it had it been sold for Rs. 890 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Selling price of a radio (SP) = Rs 990
profit (g) = 10%
Let the cost price = CP
$$\eqalign{ & {\text{CP}} = \frac{{{\text{SP}} \times 100}}{{100 + {\text{g}}}} \cr & \Rightarrow CP = \frac{{990 \times 100}}{{100 + 10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{990 \times 100}}{{110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,900 \cr & {\text{Now,}} \cr & {\text{CP}} = Rs.\,900 \cr & {\text{SP}} = Rs.\,890 \cr & {\text{CP}} > {\text{SP}} \cr & {\text{He}}\,{\text{gets}}\,{\text{loss}} \cr & = {\text{Rs}}{\text{.}}\,900 - {\text{Rs}}{\text{.}}\,890 \cr & = {\text{Rs}}{\text{.}}\,10 \cr} $$
39
A man sells an article at 10% loss. If he had sold it at Rs. 10 more, he would have gained 10% . The cost price of the article is = ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the CP1 of Article= 100x
Initial SP1 = 100x - 10% of 100x = 100x - 10x = 90x
If He sold the Article 10% profit
Now SP2 = 100x + 10% of 100x = 100x + 10x =110x
According to question
SP2 - SP1 = 10
⇒ 110x - 90x = 10
⇒ 20x = 10
⇒ x = $$\frac{1}{2}$$
Initial Cost of Article = 100 × $$\frac{1}{2}$$ = Rs. 50
40
By selling a bicycle for Rs. 2850, a shopkeeper gains 14% . If the profit is reduced to 8% then the selling price will be -
Discuss
Answer & Solution
Answer: Option B
Solution:
Let the new S.P. be Rs. x
then, 114 : 2850 = 108 : x
$$\eqalign{ & \Rightarrow x = \left( {\frac{{2850 \times 108}}{{114}}} \right) \cr & \Rightarrow x = 2700 \cr} $$