Profit and Loss Test Paper 5

21) The marked price of a radio is Rs 480. The owner allows a discount of 10% and still earns the profit of 8%. If no discount is allowed, find his gain percent?

Answer: D

Explanation:

Marked price= 480
The shopkeeper allows a discount of 10%, so, the Selling price will be= 480 * 90/100 = 432.

And the profit is 8%.

Apply formula:

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

C.P = (100/108) * 432
C.P = 400

If the discount is not allowed:
Let Profit= P%

S.P = Marked price = 480, and C.P = 400
Profit = S.P - C.P

Now, apply formula:

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

So, gain % = ((480-400)/ 400) * 100
= 80/4 = 20%

22) 5% more is gained by selling a cow for Rs 1010 than by selling it for Rs 1000. What is the C.P of the cow?

Rs 100
Rs 150
Rs 200
Rs 250

Answer: C

Explanation:

ATQ, the difference between profit % = 5
The difference between S.P = 10

Apply formula:

C.P = (100* Difference between S.P)/ (% difference in profit)

Hence, the C.P = (100 * 10)/ 5 = 200.

The difference between profit = 5%
Let the C.P = x
And S.P2= 1010, S.P1 = 1000

i.e., P2 % - P1% = 5.................................................... (i)

Apply formula of percent

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

And profit = S.P - C.P.

Now according to equation (i)

((S.P 2- x)/ x)*100 - ((S.P 1- x)/ x)*100 = 5

((1010- x)/ x)*100 - ((1000- x)/ x)*100 = 5

Or, take (100/x) as common from the whole equation.

i.e., (100/x) [(1010-x) - (1000-x)] = 5

(100/x) [1010 - x - 1000 + x] = 5

Or, (100/x) * 10 = 5

Or, 5x = 1000
Hence, x = 200, or C.P = Rs 200.

23) A dishonest milkman sells milk at cost price, but he mixes water and earns 16(2/3) % profit. Find the ratio of mixture and milk in the mixture.

7: 5
7: 6
7: 7
7: 8

Answer: D

Explanation:

Solution 1:

Let C.P of 1-litre milk = 10
Brought milk = x liters
Then C.P = 10x
Let water mixed in milk = y liter
Then quantity of mixture = (x+y) liter

Mixture is sold on C.P
Then S.P = 10(x + y)
= 10x + 10y

The profit = S.P- C.P = (10x + 10y) - 10x
= 10y
Profit % = (10y/10x)*100 = 16(2/3) %

Or, y/x = (50/3)*(1/100)
Or, y/x = (50/300)
Or, y/x = (1/6)
So, mixture = x+y = 6+1 = 7
Then, (mixture/milk) = 7/6 or 7:6

Apply formula:

Solution 2:

16(2/3) % profit = (50/3)*(1/100) = 1/6
i.e., +1>water
6> milk
That means if the total mixture is 6+1 = 7
Then milk = 6
Mixture: milk = 7: 6

24) Ayaan bought 30 kg of rice at the rate of Rs 9.50/ kg and 40 kg rice at the rate of Rs 8.50/kg and mixed them. He sold the mixture at the rate of Rs. 8.90/kg. Find his total profit or loss in the transaction.