61. Prathik sold a music system to Karthik at 20% and Karthik sold it to Swasthik at 40% gain. If Swasthik paid ₹ 10,500 for the music system, what amount did Prathik pay for the same?
63. A shopkeeper labelled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labelled price. What is the actual percent profit earned in the deal?
(a) 18%
(b) 15%
(c) 20%
(d) Can’t be determined
(e) None of these
Solution: (e)
Let the cost price of the articles be ₹100. to earn a profit of 30% he labelled them ₹ 130.
After giving a discount of 10% the selling price of the articles = 0.9 × 130 = 117
So, actual profit percent = \(\displaystyle \frac{{(117-100}}{{100}}\times 100=17\%\)
64. A man buys 4 tables and 5 chairs for ₹ 1000. If he sells the tables at 10% profit and chairs 20% profit, he earns a profit of ₹ 120. What is the cost of one table?
(a) ₹ 200
(b) ₹ 220
(c) ₹ 240
(d) ₹260
(e) None of these
Solution: (a)
Let cost of 1 table be ₹ x and cost of 1 chair be ₹ y.
65. A refrigerator and a camera were sold for ₹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
66. If the cost price of 15 articles be equal to the selling price of 20 articles, then find the loss% in the transaction.
67. The marked price of a machine is ₹ 18000. By selling it at a discount of 20%, the loss is 4%. What is the cost price of the machine?
(a) ₹ 10000
(b) ₹ 12000
(c) ₹ 14000
(d) ₹ 15000
(e) None of these
Solution: (d)
Given marked price of machine = ₹ 18000
Therefore, Discount = \(\displaystyle \frac{{20}}{{100}}\times 18000=3600\)
\(\displaystyle \Rightarrow \) SP = 18000 – 3600 = ₹ 14400
If loss of 4%, then
CP = \(\displaystyle \frac{{100\times sp}}{{100-r}}=\frac{{100\times 14400}}{{100-4}}\)
\(\displaystyle \frac{{100\times 14400}}{{96}}=15000\)
68. The profit earned after selling an article for ₹878 is the same as loss incurred after selling the article for ₹636. What is the cost price of the article?
(a) ₹ 797
(b) ₹ 787
(c) ₹ 767
(d) ₹ 757
(e) None of these
Solution: (d)
Let the C.P. of the article be ₹ x.
According to the question,
878 – x = x – 636
\(\displaystyle \Rightarrow \)2x = 878 + 636 = 1514
\(\displaystyle \Rightarrow \)x = \(\displaystyle \frac{{1514}}{2}=757\)
69. If a trader estimates his loss as 10% of the selling price, what is his real loss percent?
(a) \(\displaystyle \frac{{100}}{8}\%\)
(b \(\displaystyle \frac{{100}}{{11}}\%\)
(c) \(\displaystyle \frac{{100}}{{13}}\%\)
(d) \(\displaystyle \frac{{100}}{7}\%\)
(e) None of these
Solution: (b)
\(\displaystyle \frac{{CP-SP}}{{SP}}=\frac{{10}}{{100}}\)
10 CP = 11 SP, now let CP = 1
So CP of 11 items = 11 and SP = 10,
Loss percent = \(\displaystyle (\frac{{10}}{{11}}11\times 100)=\frac{{100}}{{11}}\%\)
70. A person sell two horses for rupees 480 each. On the first horse he gains 25 percent and on the second horse he losses 25 percent. Find the percent gain or loss in the transaction.
(a) loss 6.75%
(b) gain 6.75%
(c) loss 6.25%
(d) gain 6.25%
(e) None of these
Solution: (c)
When same quantity is sell at same price and percent
gain and loss is same then there is always loss occurred.
To calculate the loss percent = \(\displaystyle {{\left( {\frac{{Common.loss/gain}}{{10}}} \right)}^{2}}\)
i.e. \(\displaystyle {{\left( {\frac{{25}}{{10}}} \right)}^{2}}=6.25\%loss\)
