__PROFIT,LOSS AND DISCOUNT__

__PROFIT,LOSS AND DISCOUNT__

**EXERCISE 8 (A)**

QUESTION 1

**A peon purchased a chair for ₹ 700, spent ₹ 170 on its repair and ₹ 30 on the cartage.If he sold the chair for ₹ 1080, what is his gain percent ?**

Sol :

Cost price of chair = 700 + 170 + 30

= 900

Selling price of chair = 1080

Gain = Cost price – Selling price

= 1080 – 900

= 180

Gain Percent

= 20 %

QUESTION 2

**Ramesh bought 10 cycles for ₹ 500 each.He spent ₹ 2000 on the repair of all the cycles.He sold five of them for ₹ 750 each and the remaining for ₹ 550 each.What is total gain or loss %?**

Sol :

Cost price of 1 cycle = 500 ₹

Cost price of 10 cycle = 500 × 10

= 5000 ₹

Total spending on repair = 2000 ₹

Total cost price = 5000 ₹ + 2000 ₹

= 7000 ₹

Selling price of 5 cycles for ₹ 750 = 5 × 750

= 3750 ₹

Selling price of 5 cycles for ₹ 550 = 5 × 550

= 2750 ₹

Selling price of 10 cycles = S.P of 5 cycles for 750 + S.P of 5 cycles for 550

= 3750 + 2750

= 6500 ₹

Loss = Cost price – Selling price

= 7000 – 6500

= 500 ₹

Loss percentage

QUESTION 3

**By selling an article for ₹ 960 a man incurr a loss of 4%.What was the cost price of the article?**

Sol :

Cost price of article

= 1000

QUESTION 4

**If the selling price of 20 articles is equal to the cost price of 15 articles, then what is the loss percentage ?**

Sol :

Given that, a = 20 and b = 15

According to the formula,

Profit %

%

QUESTION 5

**A hawker gains the selling price of 4 ball-point pens on selling 1 dozen pens.What is his gain percentage?**

Sol :

As we know 1 dozen = 12 pens

Let the selling price of of one ball point pen be x then the profit will be equal to 4x

And the selling price of 12 pens = 12 x

Then cost price of 12 pens is equals to (C.P = S.P – profit)

Cost price of 12 pens = Selling price – Profit

C.P = 12x – 4x

C.P = 8x

Then ,

= 33.33 %

QUESTION 6

**A man bought pencils at the rate of 6 for ₹ 4 and sold them at the rate of 4 for ₹ 6. What is his gain percentage in transaction?**

Sol :

6 pencils are bought for ₹ 4

So, 1 is bought for

4 are sold for ₹ 6

So, 1 is sold for

Here, S.P > C.P , so , it is a gain

gain = S.P – C.P = 1.5 – 0.66 = ₹ 0.84

∴ gain percent

= 127%

QUESTION 7

**By selling a basket of mangoes for ₹ 105, a fruit seller loses 30%. For how much should he sell it to gain 40%?**

Sol :

As we know

….(i)

And here we know S.P = 105 ,

Loss % = 30 % and putting these in (i)

C.P = 150

Gain % = 40 and putting these two in (ii) , we get

…..(ii)

S.P = 14 × 15

S.P = 210

QUESTION 8

**A man sold a book at a loss of 20%.If he had sold the books for ₹ 12 more, he would have gained 10% .Find the cost price of the book.**

Sol :

We know that

Loss % = 20 % and in this case let the Selling Price be **x**

Putting these in (i)

…..(i)

…(ii)

…(iii)

And here we know gain % = 10 % , in this case we have Selling Price = x + 12

Putting these two in (iii) we get

…(iv)

From (ii) and (iv) , we get

Which means

3x = 12 × 8

x = 32 …(v)

putting (v) in (ii)

C.P = 40

QUESTION 9

**A trader sells two cycles at ₹ 1188 each, gaining 10% on the first cycle and losing 10% on the second cycle.What is the profit or loss percentage in the whole transaction ?**

Sol :

Case 1 (First cycle)

C.P = 1080

Case 2 (Second cycle)

C.P = 1320

S.P = 1188 + 1188

S.P = 2376

C.P = 1080 + 1320

C.P = 2400

Here , we come to know that S.P < C.P . So , it is a loss

Loss = C.P – S.P

Loss = 2400 – 2376

Loss = 24

Loss % = 1 %

QUESTION 10

**A merchant bought two calculator which together cost him ₹ 4800.He sold one of them at a loss 15% and the other at a gain of 19%.If the selling price of both the calculator is equal, find the cost price of the lower priced calculator.**

Sol :

Let the S.P. be x

We know that

also

C.P. of 1st calculator

C.P. of 2nd calculator

Now , C.P. of 1st calculator + C.P. of 2nd calculator = Total cost

x = 2380

C.P. Of 1st calculator = 2800

C.P. of 2nd calculator = 2000

C.P. of lower priced calculator = Rs. 2000

QUESTION 11

**A manufacturer sells an article to a wholesale dealer at a profit of 10%.The wholesale dealer sells it to a shopkeeper at 20% profit.The shopkeeper sells it to the customer for ₹ 56,100 at a loss of 15%.What is the cost price of the article to the manufacturer?**

Sol :

**Given :** Selling price of article = 56,100 and at loss of 15 %

We know that

Cost price of article for shopkeeper = 66,000 (Shopkeeper’s cost price)

Now , lets find C.P of article for the wholesale dealer . In this case S.P = 66000 and at a gain of 20 %

= 55000

Now , lets find C.P of article for manufacturer . In this case S.P = 55000 and at a gain of 10 %

= 50000

Cost price of the article to the manufacturer = 50,000

QUESTION 12

**A man buys a plot of agricultural land for ₹ 3,60,000. He sells one third of it at a loss of 20% and two fifth at a gain of 20%.At what price must he sell the remaining field so as to make an overall profit of 10% ?**

Sol :

C.P = 360000

To gain 10% on wholeland ,

S.P = 360000 + 10% of 360000

= 396000

of the land sold on 20% loss

S.P of land

= 96000

S.P of of the land

= 180000

Thus , S.P of the remaining land

= 39600 – 96000 – 180000

= 120000

**ALTERNATE METHOD**

S.P of total agricultural field at a profit of 10%

= 396000

So , S.P of of field

= 96000

S.P of of the field

= 180000

Hence ,

S.P of the remaining field

= 396000-96000-180000

= 120000