11. The profit earned after selling a pair of shoes for ₹ 2,033 is the same as loss incurred after selling the same pair of shoes for ₹ 1,063. What is the cost of the shoes ?
(a) ₹ 1,650
(b) ₹ 1,548
(c) ₹ 1,532
(d) Cannot be determined
(e) None of these
Solution: (b)
Let the CP of the shoes be ₹ x.
Therefore, 2033 – x = x – 163
\(\displaystyle \Rightarrow \) 2x = 2033 + 1063 = 3096
\(\displaystyle \Rightarrow \) x = \(\displaystyle \frac{{3096}}{2}=1548\)
12. Gauri went to the stationery and bought things worth ₹25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(a) ₹15
(b) ₹15.70
(c) ₹19.70
(d) ₹20
(e) None of these
Solution: (c)
Let the amount taxable purchases be Rs. x.
Then, 6% of x = \(\displaystyle \frac{{30}}{{100}}\)
\(\displaystyle \Rightarrow \) x = \(\displaystyle (\frac{{30}}{{100}}\times \frac{{100}}{6})=5\)
Cost of tax-free items = ₹ [25 – (5 + 0.30)] = ₹19.70
13. Naresh purchased a TV set for ₹11,250 after getting discount of 10% on the labelled price. He spent ₹150 on transport and ₹800 on installation. At what price should it be sold so that the profit earned would be 15% if no discount was offered?
(a) ₹12,937.50
(b) ₹14,030
(c) ₹ 13,450
(d) ₹15,467.50
(e) None of these
Solution: (d)
Cost price of TV when discount is not offered
\(\displaystyle 11250\times \frac{{100}}{{90}}=12500\)
Total cost of TV after transport and installation
= 12500 + 800 + 150 = 13450
To earn 15% profit, he must sell at
\(\displaystyle 13450\times \frac{{115}}{{100}}=15467.50\)
14. A person sold an article from ₹3600 and got a profit of 20%. Had he sold the article for ₹ 3150, how much profit would he have got?
(a) 4%
(b) 5%
(c) 6%
(d) 10%
(e) None of these
Solution: (b)
Let the cost price of the article be ₹ x
After 20% profit
\(\displaystyle \Rightarrow \) x = \(\displaystyle \frac{{120x}}{{100}}=3600\)
x = 3000
Now, profit percentage, when the article is sold for ₹ 3150
\(\displaystyle \Rightarrow \) \(\displaystyle \frac{{3150-3000}}{{3000}}\times 100-\frac{{150}}{{3000}}\times 100=5\%\)
15. A refrigerator and a camera were sold for Rs. 12000 each. The refrigerator was sold at a loss of 20% of the cost and the camera at a gain of 20% of the cost. The entire transaction results in which one of the following?
(a) No loss or gain
(b) Loss of ₹ 1000
(c) Gain of ₹ 1000
(d) Loss of ₹ 2000
(e) None of these
Solution: (b)
\(\displaystyle X+Y+\frac{{XY}}{{100}}=+20-20-\frac{{20\times 20}}{{100}}=-4\%\)
Total selling price of a refrigerator and a camera
= 12000 + 12000 = ₹ 24000
Now, loss is 4%
\(\displaystyle CP\times \frac{{96}}{{100}}=24000\)
CP = ₹ 25000
Loss amount = (25000 – 24000) = ₹ 1000
16. A milkman bought 15 kg of milk and mixed 3 kg of water in it. If the price per kg of the mixture becomes ₹ 22, what is cost price of the milk per kg?
(a) ₹ 28.00
(b) ₹ 26.40
(c) ₹ 24.00
(d) ₹ 22.00
(e) None of these
Solution : (b)
Let cost price of milk ₹ x per kg.
Price of 15kg of milk = ₹ 15x.
Now, mix 3kg of water, therefore quantity of mixture
We can also solve the equation by elimination method from options.
\(\displaystyle x\) =10 is the only option which satisfies the condition of the equation \(\displaystyle \left( {x+x-\frac{{x\times x}}{{100}}} \right)=19\)
18. A dealer marked the price of an item 40% above the cost price. Once he gave successive discounts of 20% and 25% to a particular customer. As a result, he incurred a loss of ₹ 448. At what price did he sell the item to the mentioned customer?
(a) ₹ 2416
(b) ₹ 2268
(c) ₹ 2352
(d) ₹ 2152
(e) ₹ 2578
Solution: (c) Let the cost price of the item be 100.
19. Deepak found that he had made a loss of 10% while selling his smartphone. He also found that had he sold it for Rs.50 more, he would have made a profit of 5%. The initial loss was what percentage of the profit earned, had he sold the smartphone for a 5% profit ?
