第8类RD Sharma –第13章利润损失折扣和增值税–练习13.1 |套装2

第13章利润损失折扣和增值税–练习13.1 |套装1

问题11.如果18个橙子的销售价格等于16个橙子的成本价格，找到损失百分比了吗?

解决方案：

Given, The Selling price of 18 oranges = the Cost price of 16 oranges

Let us take a as the Cost price of 1 orange

Then, the Cost price of 16 oranges will be 16a

So, the Selling price of 18 oranges will be 16a 

And, the Selling price of 1 orange will be 16a/18

We can clearly see that there is a loss

And Loss = Cost price – Selling price = a – 16a/18 = a/9

And, Loss % = (Loss/Cost price) × 100 = (a/9)/a × 100 = 11.11%

Hence, the loss percentage is 11.11%

问题12.拉维什将摩托车以28％的损失出售给了Vineet。 Vineet花费了1680卢比进行维修，然后将摩托车以35910卢比的价格卖给了Rahul，从而获得了12.5％的利润，找到Ravish的摩托车价格了吗?

解决方案：

Let a be the cost price of the motorcycle for Ravish

Given, loss % of Ravish = 28 %

So, we can conclude the Selling price of motorcycle for Ravish = a – a × 28/100 = Rs 18a/25

We know, the selling price for Ravish = The cost price for Vineet = Rs 18a/25

Also, money spend on repairing by Vineet = Rs 1680

So, the total cost price of the motorcycle for Vineet = Rs 18a/25 + Rs 1680 = Rs (18a + 42000)/25

The selling price of the motorcycle for Vineet = Rs 35910 [Given]

We can say, Profit = Selling price – Cost price

= 35910 – (18a + 42000)/25

= Rs (855750 – 18a)/25

Also, the profit % = 12.5 % [Given]

We know the formula of profit % = (profit/cost price) × 100

12.5 = [(855750 – 18a)/25] / [(18a + 42000)/25] × 100

a = 42000

Hence, the cost price of the motorcycle for Ravish is Rs 42000

问题13：通过以258卢比的价格出售书籍，书商可获得20％的收益。他应该卖出多少才能获得30％的收益?

解决方案：

Given, the Selling price of the book = Rs 258

The Gain % = 20 %

So, we can say that Cost price of book = (Selling price × 100)/(100 + Gain %) = (258 × 100)/(100 + 20) = Rs 215

Now we have to find the selling price to have a 30 % profit percentage,

So, applying the formula 

Selling price of book = [Cost price × (100 + Gain %)]/100 = [215 × (100 + 30)]/100 = Rs 279.50

Hence, the person should sell the book for Rs 279.50 in order to have a 30 % profit percentage.

问题14.售价为800卢比的有缺陷的公文包正在出售，损失了8％。如果价格进一步降低5％，找到它的售价吗?

解决方案：

Given, the Cost price of a briefcase = Rs 800

Loss % = 8 %

So, Selling price of briefcase = [Cost price × (100 – Loss %)]/100 = [800 × (100 – 8)]/100 = Rs 736

Now, the 5 % reduction in the selling price of a briefcase,

So, new Selling price = 736 – (736 × 5)/100 = Rs 699.2

Hence, the selling price of the defective briefcase is Rs 699.2

问题15：以90卢比的价格出售90支圆珠笔，一个人损失了20％。多少支圆珠笔应该以96卢比的价格出售才能获得20％的利润?

解决方案：

Given, the Selling price of 90 ball pens is Rs 160

So, we can say the selling price of 1 ball pen = Rs 160/90 = Rs 16/9 

Also, the loss % = 20 %

So, the Cost price of 1 pen can be derived as 

Cost price = (Selling price × 100)/(100 – loss%) = (16 × 100)/9 × (100 – 20) = Rs 20/9

Now for second case, profit % = 20%

And Selling price can be derived as 

Selling price = Cost price × (100 + profit %)/100 = 20 × (100 + 20)/ 9 × 100 = Rs 8/3

So, we can say with Rs 8/3 we can buy 1 ball pen 

And, with Rs 1 we can buy 3/8 pen

With Rs 96 we can buy (3 × 96)/8 pens = 36 pens

Hence, 36 ball pens would be sold for Rs 96 to have a profit of 20%

问题16.一个人以25％的利润出售商品。如果他以少20％的价格购买它，并以少36.75卢比的价格出售，他将获得30％的收益。找到文章的成本价了吗?

解决方案：

Let Rs 100 be the Cost price of the article 

Also, for the first case profit % is 5 %

So, the Selling price will be Rs 100 + 25 = Rs 125

For the second case, 

The Cost price will be 20% less than Rs 100 i.e Rs 80

Here profit % is 30 %

So, the Selling price can be derived as 

S.P = C.P × (100 + profit%)/100 = 80 × (100 + 30)/100 = Rs 104

So the difference in the Selling price in both cases is Rs 125 – Rs 104 = Rs 21

If Rs 21 is less, the Cost price is Rs 100

If Rs 1 is less, the Cost price is Rs 100/21

And if Rs 36.75 is less, the Cost price is Rs (100 × 36.75)/21 = Rs 175

Hence, the cost price of the article is Rs 175

问题17。一个不诚实的店主声称以他的成本价出售豆类，但每公斤使用的假重为950克。找到他的收益百分比?

解决方案：

Let a be the Cost price of 1000gm/1kg pulses

And as per the question, the Selling price of 950 gm pulses is also Rs a

So, the Selling price of 1000 gm pulses will be (a/950) × 1000

The gain will be Selling price – Cost price 

i.e 1000a/950 – a = 50a/950

And the Gain % = (Gain/Cost price) × 100 = (50a/950)/a × 100 = 5.26 %

Hence, the gain percentage of the shopkeeper is 5.26 %

问题18：一位经销商以3120卢比的价格购买了两张桌子。他以亏损15％的价格出售其中一张，以36％的价格出售另一张。然后，他发现每张桌子都以相同的价格出售。找出每张桌子的成本价?

解决方案：

Given, the Cost price of 2 tables is Rs 3120

Let Rs 100 be the Selling price of each table

For Table 1, 

The loss% is 15 %

So, Cost price = (Selling price × 100)/(100 – loss%) = (100 × 100)/(100 – 15) = Rs 10000/85

For Table 2,

The profit% is 36 %

So, Cost price = (Selling price × 100)/(100 + profit%) = (100 × 100)/(100 + 36) = Rs 10000/136

Ratios between two tables = 10000/85 : 10000/136 = 136 : 85

The sum of ratio’s of tables = 136 + 85 = 221

Also, the total Cost price of tables = 3120

So, the Cost price of Table 1 can be derived as Rs (3120 × 136)/221 = Rs 1920

And, the Cost price of Table 2 can be derived as Rs (3120 × 85)/221 = Rs 1200

Hence, the cost price of tables one and two is Rs 1920 and Rs 1200 respectively.

问题19. Mariam以3605卢比的价格购买了两台风扇。她卖出了一个，利润为15％，另一个则亏损了9％。如果Mariam为每个风扇获得的金额相同，请问每个风扇的成本价格是多少?

解决方案：

Given, the Cost price of 2 fans is Rs 3605

Let Rs 100 be the Selling price of each fan

For Fan1, 

The profit% is 15 %

So, Cost price = (Selling price × 100)/(100 + profit%) = (100 × 100)/(100 + 15) = Rs 10000/115

For Fan 2,

The loss% is 9 %

So, Cost price = (Selling price × 100)/(100 – loss%) = (100 × 100)/(100 – 9) = Rs 10000/91

Ratios between two fans = 10000/115 : 10000/91 = 115 : 91

The sum of ratio’s of fans = 115 + 91 = 206

Also, the total Cost price of fans = 3605

So, the Cost price of Fan 1 can be derived as Rs (3605 × 115)/206 = Rs 2012.50

And, the Cost price of Fan 2 can be derived as Rs (3605 × 91)/206 = Rs 1592.50

Hence, the cost price of fan one and two is Rs 2012.50 and Rs 1592.50 respectively.

问题20：以11卢比的价格购买了一些太妃糖，以10卢比的价格购买了9件太妃糖，如果以9卢比的价格购买了同一批太妃糖，请确定整个交易的收益或损失百分比?

解决方案：

Given, the Cost price of 11 toffees is Rs 10

So, the cost price of 1 will be Rs 10/11

Also, the Cost price of 9 toffees is Rs 10

So, the cost price of 1 will be Rs 10/9

So, we get the cost price of both toffees = (10/11) + (10/9) = 200/99

So, we can derive that the cost price of 1 toffee will be (Rs 200/99)/2 = Rs 200/198

Also, the selling price of 1 toffee is Rs 1 [Given]

We can say there is a loss, loss = Cost price – Selling price = 200/198 – 1 = 2/198

And, the loss% = (loss/cost price) × 100 = (2/198)/(200/198) × 100 = 1 %

Hence, there is a loss percentage of 1 % in the whole transaction

问题21：三轮车的销售收益为16％。如果将它的售价提高100卢比，收益将是20％。找到三轮车的CP?

解决方案：

Let Rs 100 be the cost price of the tricycle

For the first case, there is gain% of 16%

So, the selling price will be Rs 100 + 16 = Rs 116

For the first case, there is gain% of 20%

So, the selling price will be Rs 100 + 20 = Rs 120

The difference in selling prices = Rs 120 – Rs 116 = Rs 4

If the difference is Rs 4, the cost price is Rs 100

If the difference is Rs 1, the cost price is Rs 100/4

And, If the difference is Rs 100, the cost price is Rs (100/4) × 100 = Rs 2500

Hence, the cost price of the given tricycle is Rs 2500

问题22：Shabana买了16支圆珠笔，并以等于8支圆珠笔SP的损失出售了它们。找

(i)她的损失百分比?
(ii)1支圆珠笔的SP，如果她以576卢比购买了这16支圆珠笔?

解决方案：

i) Given, the number of pens bought = 16 dozens = 16 × 12 = 196 pens

Let a be the selling price of one pen

So, the selling price of 12 pens will be 192a

Also, the cost price of 8 pens is 8a

Given, the selling price of 8 pens will be equal to lose on selling 192 pens

So, we can say that loss will be 8a

The cost price of 192 pens is Rs 576

The Loss will be Cost price – Selling price

So, 8a = 576 – 192a

a = 2.88

So, the loss = 8a = 8 × 2.88 = Rs 23.04

And, the loss% = (loss/cost price) × 100 = 4 %

Hence, the loss is Rs 23.04 and the loss percentage is 4%

ii) The selling price of one pen is Rs 2.88 as derived above

So, the Selling price of 1 dozen pens will be 12 × 2.88 = Rs 34.56

Hence, the selling price of 1 dozen pens is Rs 34.56

问题23.一件衬衫的两个售价分别为利润4％和5％的差额为6卢比。

(i)衬衫的CP?
(ii)衬衫的两个售价?

解决方案：

Given, the difference between the two selling prices of shirts = Rs 6

Also, the difference in their profit percentages = 5% – 4% = 1%

i) The Cost price of the shirt will be derived as (difference in selling price × difference in profit % × 100) = 1 × 6 × 100 = 600 

Hence, the Cost price of the shirt is Rs 600

ii) And, the Selling price can be derived as 

The selling price of the first shirt = Cost price × (100 + profit%)/100 

= 600 × (100 + 4)/100 = Rs 624

 The selling price of the second shirt = Cost price × (100 + profit%)/100 

= 600 × (100 + 5)/100 = Rs 630

Hence, the selling price of the first and second shirt is Rs 624 and Rs 630 respectively

问题24.东芝以8000卢比的价格购买了100头母鸡，并以5％的收益出售了20头母鸡。她必须以多少百分比的收益出售剩余的母鸡，以便整体上获得20％的收益?

解决方案：

Given, the number of Hens is 100

The remaining number of hens is 100 – 20 = 80

Toshiba buy 100 hens for Rs 8000

So, the cost of 1 hen is Rs 8000/100 = Rs 80

And, the cost price of 20 hens will be Rs 20 × 80 = Rs 1600

Also, there is a gain% of 5%

The selling price can be (105/100) × 1600 = Rs 1680

We can say the cost price of 80 hens = 80 × 80 = Rs 6400

And the selling price of 80 hens = Rs (1600 + 6400 – 80) = Rs 7920

The gain will be Cost price – Selling price = 7920 – 6400 = Rs 1520

The gain% = (gain/cost price) × 100

= (1520/6400) × 100

= 23.75%

Hence, Toshiba must sell the remaining hens on the profit percentage of  23.75%