# Profit and Loss Test Paper 4

16) By selling a property for Rs 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15 %?

1. 55000
2. 60000
3. 57500
4. 58000

Explanation:

S.P = 45000
Loss% = 10%

Apply formula:

C.P = (100)/ (100- L %)) * S.P

C.P = (100/ (100-10))* 45000
C.P= (100/90) * 45000
C.P = 50000

Now, to gain the profit of 15%:

Apply formula:

S.P = ((100+P %) /100) * C.P

S.P = ((100+15)/100) * 50000
S.P = (115/100)* 50000

S.P = 57500

17) A person purchases some article at the rate of 4 articles for rupees 5 and sells them at the rate of 5 articles for rupees 4. Find the total profit or loss in %.

1. 22% profit
2. 20% loss
3. 40% profit
4. 36% loss

Explanation:

The C.P of 4 article is rupees 5 and selling price of 5 article is rupees 4.

Note: article ratio should be the same in both cases.

i.e.,     Article    price

C.P =      4       5

S.P =      5       4

As the article is same in both the cases, we should make the article equal.

To make article value equal, we need to multiply C.P with 5 and S.P with 4. The change made in Article should also be performed at a price to calculate the % profit or loss.

i.e.,         Article         price

C.P =       4* 5 = 20       5* 5 = 25

S.P =        5 * 4= 20       4* 4 = 16

The difference between the price of C.P and S.P is 25-16 = 9.

Now, apply % formula:

Profit or Loss % = ((difference between C.P and S.P)/ C.P) * 100

Note: if S.P > C.P = profit
If C.P > S.P = loss

Here C.P = 25, and S.P = 16

So, Loss % = (9/25) * 100 = 36%

Hence, the person incurs a loss of 36%.

18) A shopkeeper purchases some article at the rate of 2 articles for rupees 3 and purchases twice of the quantity at the rate of 3 articles for rupees 2. He sells them at the rate of 6 articles for rupees 7. Find the profit or loss %.

1. 28% loss
2. 19.04% profit
3. 22.36% loss
4. 23.52% profit

Explanation:

ATQ,

A shopkeeper purchases an article at the rate of 2 for rupees 3, and again purchase twice of the quantity at the rate of 3 for rupees 2 and the selling price of the all articles is 6 for rupees 7.

Here, the total articles are purchased in 2 times.

i.e.,     Article     price

C.P 1 =     2      3

C.P 2 =     3      2

But the shopkeeper purchases double articles the second time.
That means C.P 2 = 2 * C.P 1
So we should make the C.P 2 article's cost price as double as C.P 1

To satisfy the condition, we need to multiply the C.P 1 with 3 and C.P 2 with 4. The change made in Articles should also be performed at their price to calculate the % profit or loss.

i.e.,            Article              price

C.P 1 =      3* 2 = 6         3* 3 = 9

C.P 2 =      4* 3 = 12       4* 2 = 8

Now, we can see that C.P 2's article = 2 * C.P 1's article
Now, total article purchased by shopkeeper C.P = C.P 1 + C.P 2 = 18 at rupees 17

i.e.,      Article      price

C.P =       18       17

S.P =       6         7

Note: the article should always be equal in S.P and C.P.

To make it equal, multiply S.P with 3 and the change should also be made in the price.

i.e.,         Article      price

C.P =       18           17

S.P =      3*6=18    3* 7 = 21

The difference between the price of C.P and S.P is 21-17 = 4
Now, apply % formula.

Profit or Loss % = ((difference between C.P and S.P)/ C.P) * 100
Here C.P = 17, and S.P = 21. Selling price is more than cost price.
So, Profit % = (4/17) * 100 = 23.52%

19) A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at rupees 10 more, he had a gain of 40%. Find the C.P of the goods.

1. 500
2. 600
3. 400
4. 200

Explanation:

Let the C.P of an article is 100.
ATQ, S.P will be 110...................................................... (i)
If he has purchased it at 20% less, the new C.P = 100 - 20= 80

If the C.P is 80, then he earns a profit of 40% and sells the article at Rs 10 more than the previous price.
So, when he earns 40%, the new C.P = (40/100) * 80 = 32

That means if the C.P = 80, the S.P = 80+32 = 112............................ (ii)

Compare equation 1 and 2, and we get the difference between S.P is = 2
But ATQ, it should be 10, i.e., multiple of 5
So, we need to multiply the actual value with 5 then we get actual cost price.

Hence, the C.P of the article is = 100 * 5 = 500

20) The C.P of an article is equaled to the profit %, and a shopkeeper sells it in Rs 56. Find the C.P of the article.

1. 40
2. 60
3. 80
4. 100

Explanation:

C.P = Profit %, S.P = 56 (given)
Let C.P = Profit % = x

Apply formula:

S.P = ((100 + Profit %)/100) * C.P

56 = ((100 + x)/100) * x
x2 + 100x = 5600
x2 + 100x -5600=0

Now calculate the factors.

x2+ 140x - 40x- 5600=0
(x+140)(x- 40)=0

x= -140 and +40.
-ve value is not valid, so the x=40
So, C.P = Profit% = 40

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Profit & Loss Concepts   