CAT 2022 Slot 1 – Question 1- Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal’s cost price for syrup, in rupees per kg, is
Explanation
Let the Cost Price of Juice be rupees x per kg.
Since the Cost Price of Syrup is 20% less than the Cost Price of Juice, Cost Price of Syrup is 0.8x per kg.
Total Cost Price of Syrup = 110 * 0.8 x = 88 x
Total Coat Price of Juice = 120 * x = 120x
Total Cost Price = 88x + 120x = 208x
Since the Overall Profit Percentage is 64%.
Total Profit = 0.64(208x) = 133.12x
The profit generated on selling 10 kgs of Syrup which costs 0.8x rupees per kg at 10% Profit = 0.1 * 10 * 0.8x = 0.8x
The profit generated on selling 20 kgs of Juice which costs x rupees per kg at 20% Profit = 0.2 * 20 * x = 4x
The remaining profit (133.12x – (0.8x + 4x) = 128.32x) is generated by selling 100 kgs of Syrup and 100 kgs of Juice at ₹ 308.32 per kg.
The total Selling Price of 100 kgs of Syrup and 100 kgs of Juice is 200 * 308.32 = 2(30832)
Cost Price of 100 kgs of Syrup = 0.8x * 100 = 80x
Cost Price of 100 kgs of Juice = x * 100 = 100x
Total Cost Price = 80x + 100x = 180x
Profit = Selling Price – Cost Price
128.32x = 2(30832) – 180x
308.32x = 2(30832)
x = 200
Cost Price of Syrup per kg = 0.8 x = 0.8(200) = ₹160 per kg.
CAT 2021 Slot 3 – Question 2- A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
A.150
B.225
C.175
D.200
Explanation
Let the number of small shirts be ‘x’
then the number of large shirts becomes 64 – x.
Let the price of a small shirt be ‘y’
then the price of a large shirt becomes y + 50
Money spent on small shirts = xy = 1800
Money spent on large shirts = (64 – x) (y + 50) = 5000
(64 – x) (y + 50) = 5000
64y + 3200 – xy – 50x = 5000
64y + 3200 – 1800 – 50x = 5000
64y + 1400 – 50x = 5000
64y – 50x = 3600
32y – 25x = 1800
32y – 25(1800/y) = 1800
32y2 – 1800y – 25(1800) = 0
4y2 – 9(25)y – 25(9)(25) = 0
y = 75
Price of a small shirt = ‘y’ = 75
Price of a small shirt = ‘y + 50’ = 125
The price of a large shirt and a small shirt together, in INR = 75 + 125 = 200
CAT 2021 Slot 2 – Question 4-
Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is
A.2400
B.2200
C.2000
D.1800
Explanation
Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%.
Let‘s consider the total amount invested by the three to be ‘x’
So, 70% of (18% of x – 15% of x) = 420.
70% of 3% of x = 420
x = 20,000.
Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%.
Let’s consider the chintu’s percentage share to be ‘c’.
So, c% of 2% of 20,000 = 80.
c = 20%.
Therefore, the percentage of the amount invested by Bobby is 10%
Hence, 10% of 20,000 is 2000.
CAT 2021 Slot 2 – Question 5- Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is
A.15
B.5
C.10
D.70
Explanation
Let the total investment be P, then at the end of the first year, after a loss of x percentage the value of the investment becomes
P(1 – x)
Then in the next year the value of the investment increases by 5x
So, the overall value of the investment becomes
P(1 – x)(1 + 5x)
This is an increase of 35% from the initial investment amount.
Hence,
1.35 P = P (1 – x)(1 + 5x)
Going by the options we can see that the equation is satisfied when x = 10
Hence 10 is the answer.
CAT 2021 Slot 1 – Question 6- Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to
A.127
B.135
C.124
D.144
Explanation
Let’s consider the selling prices of small and large chocolate boxes be ‘x’ and ‘2x’ respectively.
Let’s also consider the weights of the small and large chocolate boxes to be 100(to make it easy) and y respectively.
Given that, the selling price per gram of chocolate in the large box is 12% less than that in the small box.
Therefore, x/100 x 0.88 = 2xy
y = 2000.88
y ≅ 227
Hence, the weight of chocolate in a large box exceeds 127% of that of a small box.
Hence the answer is 127.
CAT 2021 Slot 1 – Question 7-Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is
Explanation
Let’s consider the total number of pens to be
(100 +x)
Let’s consider the fixed-wage of the labour to be ‘w’
case (i): the net profit is 300
CP = 8(100 +x) + w
SP = 12 x 100 + 11 x = 1200 + 11x
Profit = SP – CP
300 = 1200 + 11x – 8(100 +x) – w
w – 3x = 100 → eq(1)
Case (ii): the net loss is 300
CP = 8(100 +x) + w
SP = 12 x 100 + 9 x = 1200 + 9x
Loss = CP – SP
300 = 8(100 +x) + w – 1200 – 9x
w – x = 700 → eq(2)
By solving equation (1) & (2) we get w = 1000.
Therefore, the wage of the employee is 1000.
Alternate solution:
We can also do this with a little intuition. The Rs 2 decrease per pen results in 300 loss from the case of 300 profit.
The net value of 600 resulted by selling the remaining pens at Rs 2 lesser.
If the number of remaining pens is x, then 2x = 600
So, x = 300.
Total pens = 100 + 300 = 400.
We can get the wage of an employee(w) by considering profit/loss
Profit = 300
100(12) + 300(11) – 400(8) -w = 300
w = 1000
CAT 2020 Slot 3Question 8- A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
A.35
B.31
C.22
D.25
Explanation
Let the price of Sugar per kilogram be ‘x’ rupees.
The man marks it up by 20% and sells 5 kilograms.
Marked Price = 1.2 × x = 1.2x
Therefore, the sale price of these 5 kgs totally would be = 5 × 1.2 × x = 6x
He then gives a discount of 10% on the markup and sells 15 kgs at that price. So, the price per kg now would be 0.9 × 1.2 × x = 1.08x
Therefore, the sale price of these 15 kgs totally would be = 15 × 1.08x = 16.2x
He then looses 3 kgs of Sugar
Therefore, the sale price of these 3 kgs = 0.
There is 35 – 5 – 15 – 3 = 12 kgs of sugar remaining.
Let’s say it is sold at px price.
So, the sale price of these 12 kgs will be = 12 × px
The overall profit for the Man is 15%, So the Sale Price of the entire 35 kgs is 35 × 1.15 × x = 40.25x
Summing up and equating all the sale prices…
40.25x = 6x + 16.2x + 0x + 12 × px
40.25x = 22.2x + 12 × px
18.05x = 12 × px
Let’s approximate this to
18x = 12 × px p = 32
= 1.5
Very importantly, px is attained after marking up the marked price.
Therefore, px = y × Marked Price
1.5x = y × 1.2x
y = 54
= 1.25
In other words we can say that the marked price was increased by 25%.
CAT 2020 Slot 2- Question 9-
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
A.60
B.50
C.55
D.54
Explanation
Let’s take Selling Price = P
= (8 × 0.8 P) + 4 × {0.8P – 14
(0.8)P}
= {(8 × 0.8 P) + 4 × (0.6P)}
Total Selling Price = 8.8 P
CP = 8.8P/1.1 = 8P (Since he makes 10% profit)
SP = 12P
So, Profit from 8P to 12P = 4P/8P
= 50%
CAT 2020 Slot 1 Question 10 – A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is
Explanation
D = Price of Desktop and L = Price of Laptop
0.2 D – 0.1 L = 2 % of 50000
0.2 D – 0.1 L = 1000
2D – L = 10000
D + L = 50000
Solving D = 20000
CAT 2019 Slot 2 Question 11-
Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was
A.2000
B.6000
C.8000
D.4000
Explanation
Let the cost price of one bicycle = Rs. x
Total cost price = Rs. 10x
He made a total profit of 25% on 6 cycles and 25% loss on 4 cycles and made a profit of Rs. 2000
So, 2000 = 6 x – 4 x
2000 =
x = Rs. 4000
CAT 2019 Slot 2 Question 12-
A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x -y) / p equals
A.1
B.1.2
C.0.7
D.0.50
Explanation
The Shopkeeper procures the table at price ‘p’
He gains 20% on the transaction with Amal
So, Amal buys the table at ‘1.2p’
Amal sells athe table at 30% profit,
So the Selling Price of Amal = 1.3 * 1.2p = 1.56p
x = 1.56p
The Shopkeeper looses 20% on the transaction with Asim
So, Asim buys the table at ‘0.8p’
Asim sells athe table at 30% loss,
So the Selling Price of Asim = 0.7 * 0.8p = 0.56p
y = 0.56p
(x-y)/p = (1.56p – 0.56p)/p = 1.
CAT 2019 Slot 1 Question 13-
On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?
A.80
B.85
C.100
D.95
Explanation
From the question, let us frame the following equations
-P x 5% + b x 15% = 7 —(1)
P x 5% + b x 10% = 13 — (2)
________________________
(+)
b x (25%) = 20
Price of Book = b = Rs. 80
CAT 2017 Slot 2 Question 14-
The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is
A.1500
B.2000
C.2500
D.3000
Explanation
given that the manufacturer of a table sells it to the whole sale dealer at a profit of 10%
CAT 2017 Question Paper Quants Slot 2 Profit and Loss
Then the whole sale dealer sells to a retailer at a profit of 30%
CAT 2017 Question Paper Quants Slot 2 Profit and Loss
The retailer sells to a customer at a profit of 50%
CAT 2017 Question Paper Quants Slot 2 Profit and Loss
If the customer pays Rs.4290 for the table then 1.1 × 1.3 × 1.5X = 4290
⟹ 1110
× 1310
× 32
X = 4290
⟹ X = 4290 × 1011
× 1013
× 23
X(Manufacturing cost) = Rs. 2000
The question is “The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is”
Hence, the answer is 2000
Choice B is the correct answer
CAT 2017 Slot 2 Question 15-
Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?
A.50
B.30
C.25
D.45
Explanation
Given that Mayank buys some candies for Rs.15 a dozen and equal number of different candies for Rs.12 a dozen.
Let us assume that there are n dozens,
Cost price of the candies = 15n + 12n = 27n
In total he buys 2n dozens of candies.
A dozen is sold at Rs.16.50
Selling price of candies = 2n × 16.50 = 33n
Profit = Selling price – Cost Price
Profit = 33n – 27n = 6n = 150
n = 1506
= 25
Therefore the no. of candies Mayank bought altogether is 2n = 2 × 25 = 50 dozens
