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All questions of Profit, Loss and Discount for CAT Exam

A sells a car to B at 10% loss. If B sells it for Rs. 54000 and gains 20%, the cost price of the car for A was
a)Rs. 25000
b)Rs. 50000
c)Rs. 37500
d)Rs. 60000
Correct answer is option 'B'. Can you explain this answer?

Gaurav Datta answered
Selling price of the car = Rs.54,000
gain 20%
Friend's cost price of the car = Rs. 54000 x 100/120 = Rs.45,000
Now selling price of the car of the first owner Rs.45000
Loss 10%
Cost price of the car = 45000 x 100/90
= Rs.50,000

John buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, what is his gain percent ?
  • a)
    12%
  • b)
    10%
  • c)
    4 + 4 / 7%
  • d)
    5 + 5 / 11%
Correct answer is option 'D'. Can you explain this answer?

Whenever we get this type of question, we should have formula in mind that,
Gain% = (gain/cost) x 100

Cost = 4700 + 800 = Rs. 5500
S.P. = Rs. 5800

Profit = 5800 - 5500 = 300

Sunny marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance which reads 800 gms for 1000 gms. What is his net profit/ loss percentage?
  • a)
    37.5%
  • b)
    57.2%
  • c)
    8%
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Ravi Singh answered
Since he sells the goods at a discount the selling price will be (40% - 10%) = 30% profit.
The profit is 30%.
Lets take the buying price as x.
The profit on the 1000g rather 1 kg will be 30% of x.
This gives us 0.3x
In reality this is the profit for 800 g.
The profit he gets for 1000g will be :
1000/800 × 0.3x = 0.375x
To change this to percentage it becomes :
0.375x/x × 100% = 37.5
The overall percentage profit gained by the seller will be given as : 37.5%

A man sells a TV set for Rs. 33000 and makes a profit of 10%. He sells another TV at a loss of 20%. If on the whole, he neither gains nor loses, find the selling price of the second TV set.
  • a)
    Rs.15,000 
  • b)
    Rs.30,000
  • c)
    Rs.12,000
  • d)
    Rs.27,000
Correct answer is option 'C'. Can you explain this answer?

Ishani Rane answered
Let's denote the cost price of the first TV as CP1, the cost price of the second TV as CP2, and the selling price of the second TV as SP2.

The man makes a profit of 10% on the first TV, so we can write the selling price of the first TV as:

SP1 = CP1 + 10% of CP1
33000 = CP1 + 0.1 * CP1
33000 = 1.1 * CP1
CP1 = 33000 / 1.1
CP1 = 30000

He sells the second TV at a loss of 20%, so we can write the selling price of the second TV as:

SP2 = CP2 - 20% of CP2
SP2 = 0.8 * CP2

Since he neither gains nor loses on the whole, the total cost price equals the total selling price:

CP1 + CP2 = SP1 + SP2

We already know the values of CP1 and SP1, so we can substitute them in the equation:

30000 + CP2 = 33000 + SP2

We also know that SP2 = 0.8 * CP2, so we can substitute that as well:

30000 + CP2 = 33000 + 0.8 * CP2

Now, we can solve for CP2:

0.2 * CP2 = 3000
CP2 = 15000

Now that we have the cost price of the second TV, we can find its selling price using the relation we found earlier:

SP2 = 0.8 * CP2
SP2 = 0.8 * 15000
SP2 = 12000

So the selling price of the second TV set is Rs. 12000.

E sold at table to R at a profit of 25%.R sold the same table to S for Rs. 90 thereby making a profit of 20%. Find the price at which E bought the table from Z if it is known that Z gained 25% in the transaction.
  • a)
    Rs.80 
  • b)
    Rs.75 
  • c)
    Rs.90 
  • d)
    Rs.60
Correct answer is option 'D'. Can you explain this answer?

R sold the table at 20% profit at Rs. 90. Thus cost price would be given by: CPR X 1.2 = 90
R’s Cost price = Rs. 75.
We also know that E sold it to R at 25% profit. Thus,
E’s Cost price X 1.25 = 75
-> E’s cost price = 60. 

On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. What is the cost price of a ball?
  • a)
    Rs. 43
  • b)
    Rs. 60
  • c)
    Rs. 55
  • d)
    Rs. 34
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
Let the cost price of a ball be Rs. x.
So, the CP of 17 balls is Rs. 17x.
The CP of 5 balls is Rs. 5x.
 
Since Loss = CP - SP
So, 5x = 17x - 720
On solving, we get
12 x = 720
that is, x = 60
So, the cost price of a ball is Rs. 60.

Murali purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. Find out his profit percentage.
  • a)
    3.5
  • b)
    5.6
  • c)
    4.1
  • d)
    3.4
Correct answer is 'B'. Can you explain this answer?

The cost price of 20 dozens of toys = 375*20 i.e per dozen 375= Rs 7500/-the selling price of one dozen toys = 12*33= Rs 396/-the selling price of 20 dozen toys = 396*20= Rs 7920/-gain=sp-cp = 7920-7500 =Rs.420/-gain%=(gain/cp)*100 = 420/7500*100 =5.6%

Read the passage below and solve the questions based on it, Patna-mart, sister concern of Wal-marL is planning to establish a mechanism to give discount, it is actually a Kind Ja Simsim kind of game where if you win any round, you will gel some discount specific to dial round, and it you lose, you will be losing al! the discounts so far won.
Now, round l is hav ing discount coupons of 2%.
Round 2 is having discount coupons of 4%.
Round 3 is having discount coupons of 6%, And so on...............
There are infinite round sand you can participate in all the rounds but you can participate in any round only once and before participating in round N (any particular round), you should have participated in round 1 - round N -1 (all die rounds before that particular round.) All the discounts won will be successive, eg., if you win Round 1 and then round 2 also, you will get a successive discount of 2% and then 4%. But again as the rule goes on. if you lose round 3, you will be losing ail the discount coupons won so far Bui despite losing round 3, you can participate in round 4 and hence.
Q.
What is the minimum number of rounds to obtain maximum possible discount?
  • a)
    50
  • b)
    100
  • c)
    Infinite
  • d)
    Cannot be determined
Correct answer is option 'A'. Can you explain this answer?

Anaya Patel answered
Maximum possible discount in any case can be only 100% and any discount more than 100% is actually 100% only. Now, whatever is the discount, till the moment we get a discount of 100%, value of the article cannot be zero (even infinite discounts of 99.99% won’t make it equal to a discount of 100%) So, number of rounds needed to obtain 100% discount = 50.

A man sells an article at 10% above its cost price. If he had bought it at 15% less than what he paid for it and sold it for Rs. 33 less, he would have gained 10%. Find the cost price of the article.
  • a)
    Rs.400 
  • b)
    Rs.200
  • c)
    Rs.325
  • d)
    Rs.260
Correct answer is option 'B'. Can you explain this answer?

Surbhi Joshi answered
Given:
Selling price = Cost price + 10% of cost price
Let the cost price be x
Selling price = 1.1x

To find:
Cost price of the article

Solution:
Let the original selling price be y
The cost price of the article if he had bought it at 15% less than what he paid for it = 0.85y
He sold it for Rs. 33 less, so the selling price = y - 33
He gained 10%
Selling price = Cost price + 10% of cost price
1.1x = 1.1(0.85y) + 0.1(0.85y)
1.1x = 0.935y + 0.085y
1.1x = 1.02y
y = 1.078x

Substituting the value of y in the equation y - 33 = 1.1(0.85y)
1.078x - 33 = 0.935y
1.078x - 33 = 0.935(1.078x)
1.078x - 33 = 1.00883x
0.06917x = 33
x = 33/0.06917
x = Rs. 476.86

Therefore, the cost price of the article is Rs. 476.86
But, the options given are not in decimals
So, the closest option to Rs. 476.86 is Rs. 200

Hence, the correct option is (B) Rs. 200.

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x
  • a)
    15
  • b)
    25
  • c)
    18
  • d)
    16
Correct answer is 'D'. Can you explain this answer?

Sameer Rane answered
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.S.P. of x articles = Rs. 20.Profit = Rs. (20 - x).because [(20 - x)/x] x 100 = 25=> 2000 - 100x = 25x=> 125x = 2000 x = 16.

Read the passage below and solve the questions based on it, Patna-mart, sister concern of Wal-marL is planning to establish a mechanism to give discount, it is actually a Kind Ja Simsim kind of game where if you win any round, you will gel some discount specific to dial round, and it you lose, you will be losing al! the discounts so far won.
Now, round l is hav ing discount coupons of 2%.
Round 2 is having discount coupons of 4%.
Round 3 is having discount coupons of 6%, And so on...............
There are infinite round sand you can participate in all the rounds but you can participate in any round only once and before participating in round N (any particular round), you should have participated in round 1 - round N -1 (all die rounds before that particular round.) All the discounts won will be successive, eg., if you win Round 1 and then round 2 also, you will get a successive discount of 2% and then 4%. But again as the rule goes on. if you lose round 3, you will be losing ail the discount coupons won so far Bui despite losing round 3, you can participate in round 4 and hence.
Q.
What is the minimum possible discount after 20 rounds provided that customer has won a minimum of 18 rounds?
  • a)
    100%
  • b)
    50%
  • c)
    0%
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

If he loses in 19 th round, all previous 18 round wins gets cancelled. Hence assuming he loses 20 th round minimum discount will be zero and maximum can be 2 % if he wins it. so answer is C

When an item is sold for Rs. 18,700, the owner loses 15%. At what price should that plot be sold to get a gain of 15%?

  • a)
    Rs. 25100
  • b)
    Rs. 24200
  • c)
    Rs. 25300
  • d)
    Rs. 21200
Correct answer is option 'C'. Can you explain this answer?

Avi Shah answered
First we find CP.

If SP is Rs. 85 then CP = Rs 100

If SP is Rs. 18,700, then

CP = = Rs 22,000

Now, if CP is Rs 100, then SP = Rs. 115

Thus, if CP is Rs. 22,000, then

SP = =Rs 25,300

Read the passage below and solve the questions based on it, A shop has the following discount layers 1st layer - Buy Jn get 2 free. 2nd layer - Buy 2, get 3 free. 3rd layer - Buy 3, gel 4 free And so on there are infinite layers on the same pattern
Q.
For how many of these discount layers discount percentage offered is more than 50%?
  • a)
    4
  • b)
    27
  • c)
    99
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Anaya Patel answered
Since in all these cases, more articles are given free than the purchased article, so the net discount is more than 50%. Hence in all these layers, the discount offered is more than 50%. (If the articles given free is equal to the articles purchased, discount percentage will be equal to 50%).

Murali purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. Find out his profit percentage.
  • a)
    3.5
  • b)
    5.6
  • c)
    4.1
  • d)
    3.4
Correct answer is option 'B'. Can you explain this answer?

Arya Roy answered
Cost Price of 1 toy = Rs.375/12 = Rs. 31.25

Selling Price of 1 toy = Rs. 33

So, Gain = Rs. (33 - 31.25) = Rs. 1.75

Profit % = [(1.75/31.25) x 100 ]% = 28/5 % = 5.6%

 Read the passage below and solve the questions based on it Newspaper major The Asian Times is dying to enter the city of Paperabad. where already two newspapers The Deccan
City and Good Morning Pape rah ad are in circulation. The population of the city is 35 lakhs of which, according to the recent survey, 60% read newspaper. The two evening newspapers sell at Rs 1.75 per copy on weekdays and Rs3.00 per copy on Sundays. The Asian Times promised its readers newspapers at Rs 1.50 per copy per day. Since people w'crc aware of the quality7 of the paper, the management thought that it can capture a major chunk of the newspaper reading population. On weekdays, the operational cost of the The Asian Times w-crc Rs 62.500 per day and the cost for the material and printing charges was Rs 2.75 per newspaper. For the Sunday edition the cost of the newspaper per copy was Rs 3.00 and the operational cost were Rs 75,000. The number of the copies of tire newspaper The Asian Tunes sold on Sunday was 16.66% less than the number of copies sold on any of the week days. The number of copies sold on any weekday being the same. The amount collected through the advertisement on any weekday was the same and equaled Rs 2.50,000 per day while for Sunday it was 4.35.000.
Q.
If 50,000 of the readers of The Deccan City now read The Asian Times on all weekdays, how much profit would The Asian Times expect to make every week?
  • a)
    2,55,000
  • b)
    3,85,000
  • c)
    4,57,000
  • d)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?

Preeti Khanna answered
Since we are not having any information regarding the total number of copies sold (the information is talking about the reader of “The Deccan City”), we cannot determine the profit.

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x
  • a)
    15
  • b)
    25
  • c)
    18
  • d)
    16
Correct answer is option 'D'. Can you explain this answer?

Dhruv Mehra answered
Let the Cost Price of one article = Rs. 1
CP of x articles = Rs. x 
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
⇒ (SP - CP) / CP = 25 / 100 = 1/4 ⇒ (20-x) / x = 1/4
⇒ 80−4x=x
⇒ 5x=80
⇒ x = 80/5 = 16

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