QUESTIONS ON PROFIT & LOSS (PART-III)

QUERY 21

A person bought some oranges at the rate of 5 per rupee, he then bought the same number of oranges at the rate of 4 per rupee. He mixes both the types and sells at 9 for 2 rupees, in this business he bore a loss of Rs 3, find out how many oranges he bought in all ?

A) 1000
B) 1100
C) 1150
D) 1180

MAHA GUPTA
It will be easier if the number of bought items of each kind is taken equal to the LCM of each. LCM of 5 and 4 = 20

So, let each kind of oranges bought = 20
Therefore the cost price (CP) of oranges 5 per rupee = 20/5 = Rs 4
and the CP of oranges 4 per rupee = 20/4 = Rs 5

Therefore total CP = 4+5 = Rs 9

Now, the total number of oranges bought = 20+20 = 40.
But all the oranges were sold at 9 for Rs 2

So the selling price (SP) = 40*2/9 = Rs 80/9
Therefore the loss = CP – SP = 9 – 80/9 = 1/9

But actual loss is Rs 3

Now, if 1/9 is the loss the number of oranges in all bought = 40
If 3 is the loss the number of oranges in all bought = 40*9*3 = 1080 (option ‘D’)

QUERY 22

A person bought 2 bicycles for Rs 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get Rs 5 more. the difference of cost price of the two bicycles was?

A) Rs 50
B) Rs 40
C) Rs 35
D) Rs 75

MAHA GUPTA
To do this quickly use hit and trial method mixing it with your common sense. You see the profit is more in the second deal; and this more profit is only due to increase in the %age profit of the first item; means the price of the first bicycle is more than the second one.

Ok; for easier calculations let the difference in prices is Rs 200; means the price of the first bicycle is Rs 900 and price of the other is 700.

According to the question, profit in the first deal = 10% of 900 + 20% of 700 = Rs 230
And profit in the second deal = 20% of 900 + 10% of 700 = Rs 250
Therefore increase in profit = Rs 20

But the actual increase in profit = Rs 5

Now, if the increased profit is Rs 20 the difference in prices = 200
If increased profit is Rs 5 the difference in prices = 50 (option ‘A’)

QUERY 23

A lady bought 30 kg of wheat at the rate of 9.50 per kg; and same quantity of wheat at the rate of 8.50 per kg and mixed them. She sold the mixture at the rate of 8.90 per kg. Her total profit or loss in the transaction was?

A) profit of Rs 6
B) profit of Rs 7
C) loss of Rs 6
D) loss of Rs 7

MAHA GUPTA
She bought 30+30 = 60 kg of wheat
Cost Price (CP) of the wheat = (30*9.30) + (30*8.30) = 285 + 255 = 540

Selling Price (SP) of 60 kg of wheat = 60*8.90 = 534

As the SP is less than the CP it’s a loss
So loss in the transaction = CP – SP = 540 – 534 = Rs 6 (option ‘C’)

QUICKER APPROACH
As the wheat bought both times equal, the buying rate = (9.50 + 8.50)/2 per kg = 9 per kg

Selling rate = 8.90 per kg

So, it’s a loss of 9 – 8.90 = 0.10 = 1/10 per kg

Hence loss on 60 kg = 60*1/10 = Rs 6 (option ‘C’)

QUERY 24

By how much more percentage a shopkeeper should mark the price above the cost price of an article so that he may earn profit at 5% even after two successive discounts of 20% and 10%?

A) 45.76%
B) 45.83%
C) 46%
D) 46.15%

MAHA GUPTA
Let the cost price (C. P.) = 100
Then the selling price (S. P.) = 105 (as the profit after discounts is given 5%)

The discounts are on the marked price; and they are successive discounts
So the effective discount = (20+10) – (20*10)/100 = 28%

Now, let the marked price = x
It means 100 – 28 = 72% of x = 105
Therefore x (marked price) = 145.83 (appox)

But the cost price = 100 (as assumed above)
Hence the shopkeeper should mark the price above cost price by = 145.83 – 100 = 45.83 which is 45.83% of the cost price (option ‘B’)

QUERY 25

A man purchased one type of oranges at Rs 4 per 10 oranges and some other type of oranges at Rs 3 per 15 oranges. He mixes them all and sells at the profit of 20%. Find the selling price of oranges at Re 1.

A) 2.97
B) 2
C) 3.35
D) 3

MAHA GUPTA
Cost price of 10+15 = 25 oranges = 4+3 = Rs 7
The profit the person wants = 20%
Therefore the selling price of 25 oranges = 7 + 7*20/100 = Rs 8.40

Therefore the selling price of the oranges per Rupee = 25/8.40 = 2.97 oranges (option ‘A’)

QUERY 26

A book seller bought 200 books for Rs.12000. He wanted to sell them at a profit so that he got 20% books free. At what profit percent should he sell them?

A) 15%
B) 20%
C) 23%
D) 25%

MAHA GUPTA
The shopkeeper wants 20% books free as his profit; means 20% of 200 i.e. 40 books

Cost price of 200 books = 12,000
Therefore cost price of 40 books = 2,400

Means he wants a profit of Rs 2,400 on Rs 12,000
Therefore profit in %age = (2,400/12,000)*100 = 20 (option ‘B’)

QUERY 27

A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gain 35%. The marked price is above the cost price by?

A) 40%
B) 39%
C) 50%
D) 20%

MAHA GUPTA
Let the C.P. of each article = Rs 100
As the gain in the end is 35%, the selling price of each article = Rs 135

Because the tradesman is giving 1 article free for every 15 articles, we need to know the C.P. of 16 articles and then know the S.P. of 15 articles assuming that C.P of 15 articles.

Now C.P. of 16 articles = 16*100 = 1,600

Therefore, S.P. of 15 articles = 1,600*135/100 = 2,160
Hence, S.P. of each article = 2,160/15 = 144

Now, if S.P. of each article is Rs 96 (as the discount on the marked price is 4%), marked price = 100
If S.P. of each article is 144, marked price = (100/96)*144 = 150

Thus, marked price = 50% above C.P. (option ‘C’)

QUERY 28

A sells a horse to B at a profit of 5% and B sells it to C at a profit of 10%. If C pays Rs 855 for it, at what price did A buy?

A) Rs 740.26
B) Rs 750
C) Rs 750.86
D) Rs 733.15

MAHA GUPTA
B’s selling price = C’s cost price = 855
So, B’s cost price = (100/110)*855

A’s selling price = B’s cost price = (100/110)*855
So, A’s cost price = (100/105)*(100/110)*855
= 740.26 Appox (option ‘A’)

QUERY 29

The cost price of 20 articles is the same as the selling price of x articles. If profit is 25%; then the value of x is?

A) 13
B) 16
C) 19
D) 25

MAHA GUPTA
Let CP of each article = Re 1
Therefore CP of ‘x’ articles = Rs x
SP of x articles = Rs 20 (given)

Hence the profit = SP – CP = 20 – x

Therefore [(20 – x)/x]*100 = 25
=> 2000 – 100x = 25x
=> x = 16 (option ‘B’)

QUERY 30

By selling 45 lemons for Rs 40 a man loses 20%. How many should he sell for Rs 24 to gain 20% in the transaction?

A) 18
B) 20
C) 16
D) 19

MAHA GUPTA
SP of 45 lemons = 40
As he sells them at 20% loss, so the CP of 45 lemons = (100/80)*40 = 50
Hence CP of 1 lemon = 50/45

SP of the new transaction = 24
But he wants gain of 20% now
So the CP now must be = (100/120)*24 = 20 (option ‘B’)

Now if CP is 50/45 the number of lemon = 1
If CP is 20 then the number of lemons = (45/50)*20 = 18 (answer)