Sign in
Please select an account to continue using cracku.in
↓ →
The cost price of a toy is Rs . 225. The marked price is twice of the cost price. What will be the discount offered to get profit of 56% on the sale of the toy?
CP = Rs. 225
MP = 2*225 = Rs. 450
Now, to get a profit of 56%, the toy must be sold for 156% of its cost price:
Hence, SP = 225*1.56 = Rs. 351
Discount = MP - SP
Discount = Rs. 450 - Rs. 351 = Rs. 99
Discount % = $$\dfrac{99}{450}\times100=22\%$$
A fruit seller bumps up the cost price of apples per kg by 50% and then gives a discount of 20%, to sell apples at the rate of 72 per kg. What is the cost price of the apples per kg?
The Marked Price of apples per kg = 72/.8 = Rs 90
The Cost price of apples per kg = 90/1.5 = Rs 60
If by selling 20 apples the shopkeeper gains the cost price of 4 apples, find the gain%.
SP of 20 apples - CP of 20 apples = CP of 4 apples
SP of 20 apples = CP of 24 apples
SP of 1 apple/CP of 1 apple = 24/20 = 1.2
Profit % = (1.2-1)*100 = 20%
A vendor buys a book at Rs 120 and marks it at Rs 145. When a regular customer visits the shop, the vendor gives him a discount of 25%. What is the price at which the customer gets the book?
The discount is calculated on the the marked price always. So, the selling price is 145 - 145 * 25% = Rs. 108.75
If a seller earns a profit of 30% by selling a product on a selling price of Rs. 1200. What will be the cost price of the product?
As we know that selling price of the product is Rs. 1200
Let’s say cost price of the product is x
Now after making a profit of 30%, selling price will be = $$x \times 1.3$$ = 1.3x
So 1.3x = 1200
x= $$\frac{1200}{1.3}$$ = 923
The shopkeeper marked an article 30% above the cost price and sold it a discount of 20%. If he made a profit of Rs. 60. Find the cost price of the article.
Let the cost price be c.
The marked price of the article will be 1.3c
If a discount of 10% is offered the selling price will be 1.3c * (0.8) = 1.04c
Profit = 0.04c = 60
C = 1500
Hence, the cost price is Rs. 1500
If a sum of 36 rupees amounts to 48.24 rupees after two years under simple interest, then what will 63 rupees amount to in three years at the same S.I?
Let the rate of interest = r
==> 36(1+2r/100) = 48.24
==> r = 17%
63 rupees after three years = 63(1+3r/100) = 95.13 rupees.
So, the correct option to choose is B.
Kiran deposited Rs 50000 in a bank at a simple interest rate of 20% for 3 years. How much more interest would she have accrued if she were to deposit the same amount at the same interest rate for the same period at compound interest?
Interest at simple interest = P X r X t/100 = (50000 X 20 X 3)/100 = Rs 30000
Interest at compound interest = $$P[(1+\frac{r}{100})^n - 1] = 50000[(1.2)^3 - 1] = 36400$$
So, the difference is Rs 6400.
If the difference in compound interest and simple interest for a principal amount of 5000 with a rate of 10% is 50. Find the duration for which interests were calculated?
We should try it by putting up the values given in the option.
As putting up duration = 2 years, Simple Interest = 5000*10*2/100 = 1000
And compound interest will be = 5000(110/100)(110/100) = 1050
Hence answer will be b
Arjun borrowed some money at the rate of 9% per annum for the first 3 years, at the rate of 6% per annum for the next 2 years and at the rate of 14% for next 4 years. If he pays a total simple interest 2280, how much did he borrow?
Let the amount borrowed by Arjun be x.
SI = $$\frac{PRT}{100}$$
Given,
$$\frac{9*x*3}{100} + \frac{6*x*2}{100}+\frac{14*x*4}{100} = 2180$$
$$\frac{95*x}{100} = 2280$$
x = 2400
Option C
The cost of running a movie theatre is Rs . 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show.
For all shows together, total occupancy was 80%. What was the maximum amount of profit possible?
The total cost consists of a fixed daily fee plus a per-show fee: Daily fixed cost: Rs. 10,000
Cost for 3 shows: 3*5,000 = Rs. 15,000
Total Cost: 10,000 + 15,000 = Rs. 25,000
The theatre has 200 seats and runs 3 shows, meaning there are 600 total available seats.
Total occupancy (80%): 0.80*600 = 480
To maximise profit, we want the most expensive tickets to sell out first.
Show 1 (Rs. 250): Max capacity = 200 viewers.
Show 2 (Rs. 250): Max capacity = 200 viewers.
Show 3 (Rs. 200): Remaining viewers = 480 - (200 + 200) = 80 viewers.
First two shows: 400 × 250 = Rs. 100,000
Late-night show: 80*200 = Rs. 16,000
Total Revenue: 1,16,000
Profit = Revenue - Cost
Profit = 1,16,000 - 25,000 = Rs. 91,000
Archit invested an amount of Rs. 13,900 divided into two different schemes, A and B, at the simple interest rate of 14% p.a. and 11% p.a., respectively. If the total amount of simple interest earned in 2 years is Rs. 3508, then determine the amount invested in Scheme B by Archit?
Let the amount invested in Scheme A be Rs. X.
Then, the amount invested in Scheme B = 13900 - X
Interest from Scheme A: $$\dfrac{\left(X\times14\times2\right)}{100}=0.28X$$
Interest from Scheme B: $$\dfrac{\left(\left(13,00-X\right)\times11\times2\right)}{100}=0.22\left(13900-X\right)$$
Total interest: 0.28X + 0.22(13900 - X) = 3508
0.28X + 3058 - 0.22X = 3508
0.06X = 450
X = 7500
Amount in Scheme B: 13900 - 7500 = 6400
A dealer has 1000 kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit he earns is 14%. What is the quantity which is sold at 18% profit ?
Let the cost price be 100x.
Let the part sold at 8% profit be K kg. So, part sold at 18% profit would be (1000-K) kg
Total profit = $$\ \frac{\ SP\ -\ CP}{CP}\times\ 100$$ = $$\ \frac{\ 108x\times K\ +\ 118x\left(1000-K\right)\ \ -\ 1000\times\ 100x}{1000\times\ 100x}\times\ 100$$ = 14
On solving it, we get K=400kg.
Quantity sold at 18% profit = 1000-K = 600 Kg.
So, option E is the answer.
A milkman mixes 2 litres of water for every 6 litres of milk. The cost price of 1 litre of milk is Rs. 80. He marks up the price of the milk by 20% and gives a discount of 10% to the customers. Find the net profit percentage of the milkman.(Assume the cost of water to be negligible)
Given the milkman mixes 2 litres of water for every 6 litres of milk.
As the cost of water is negligible, the cost price of 8 litres of mixture is 6*80 = Rs. 480.
And the cost price of 1 litre of mixture is $$\frac{480}{8}=60$$.
Now he marks up the cost price of milk by 20% i.e.
So, the marked price of 1 litre of milk is $$80\times\left(1+\frac{20}{100}\right)=96$$
And he gives a discount of 10%,
So the selling price of 1 litre of milk is $$96\times\left(1-\dfrac{10}{100}\right)=86.4$$
Hence, the profit percentage is $$\frac{86.4-60}{60}=\frac{26.4}{60}=44\%$$
Hence, the answer is 44%.
A book was sold at a price of 450 rupees after giving a discount of 25%. Instead of giving a discount, if the book seller sold it at a premium of 12.5%, find the selling price of the book.
We have the original selling price as 450, and we are given that this was after a 25% discount, that means the original price would be,
$$\frac{450}{0.75}=600$$
We are now asked the new selling price if it is sold at a 12.5% profit,
0.125 is nothing but one eighth, $$\frac{600}{8}=75$$
So, the final selling price is 675 rupees.
While selling, a shopkeeper uses a weighing machine that shows 20% more than the actual weight and uses a normal machine while buying. He buys 50 gm of dal for Rs. 2 and a customer buys 24 gms for Rs. 1. If he professes to sell 24 gms, what is his profit percentage ?
He claimed to sell 24gms. But the actual amount he sold will be different.
According to the faulty weighing 24 gms is 120% of actual weight.
The actual weight he sold will be $$\frac{24}{1.2}=20$$
C.P of 20 gm = $$2\cdot\frac{20}{50}=\frac{4}{5}$$
We are told that S.P of 24 gms is Rs. 1.
Profit percent = $$\dfrac{\left(1-\dfrac{4}{5}\right)}{\dfrac{4}{5}}$$ = 25%
The selling price of 12 pens is equal to the cost price of 15 pens. If the selling price is increased by 10%, what would be the next profit percentage on selling one pen?
Let's take the selling price and cost price of 1 pen to be $$s$$ nd $$c$$ respectively.
We have the equation $$12s=15c$$, which would give te ratio of selling price to cost price as $$\frac{s}{c}=\frac{15}{12}=\frac{5}{4}$$
Essentially, if the cost price is 4, the selling price is 5
If we increase the selling price by 10%, it becomes 5.5
This would give us a profit of 1.5 per pen
Profit percentage would be $$\frac{1.5}{4}\times\ 100=1.5\times\ 25=37.5\%$$
Therefore, Option D is the correct answer.
Anul took a certain amount on a loan from the bank at 15% simple interest. He invests the amount in two halves at interest rates of 10% and 20% compounded annually. Anul takes his investments out after two years and pays back the bank's principal amount and interest. Investing the remaining amount at 20% compound interest rate (annually). What would be Anul's net profit percentage after 3 years since he first borrowed the amount from the bank?
Let's take the amount borrowed by Anul to be 100
The interest paid by Anul to the back would be $$\frac{100\times\ 15\times\ 2}{100}=30$$, hence net amount paid back to the bank: 130
His 50 invested at 10% compound interest would turn to $$50\left(1.1\right)^2$$, and the 50 invested at 12% compound interest would turn to $$50\left(1.2\right)^2$$
Giving the final amount with him to be $$50\left[\left(1.1\right)^2+\left(1.2\right)^2\right]=50\left[1.21+1.44\right]=50\left(2.65\right)$$
Giving the net amount with Anul at the end of two years to be 132.5
This gives a net profit of 2.5 after paying back the amount of 130 with interest to the bank.
Investing this money at 20% interest rate for one more year, Anuwl would have a total of $$2.5\times\ 1.2\ =\ 3$$
Hence 3% profit.
Aman lends Rs.1,00,000 to Raghu at a rate of 20% compounded annually. At the same time, Ram lends Rs. 1,00,000 to Aman at a rate of 15% simple interest. Find the net profit for Aman, if both Raghu and Aman pay back the entire amount after 3 years.
Total amount paid back by Raghu to Aman = $$100000\left(1.2\right)^3=172800$$
Total amount paid back by Aman to Ram = $$100000\left(1+3\times\frac{15}{100}\right)=100000\left(1.45\right)=145000$$
Hence, the net profit of Aman is 172800-145000 = Rs. 27800
Hence, the answer is Rs. 27800.
Kushal borrowed ₹82,000 from HSBC under a unique repayment scheme. He plans to repay the loan over two years, with the payment at the end of the second year being three times the amount paid at the end of the first year. Given that the interest rate is 10% compounded annually, calculate the total interest paid over the two years.
Using the installments formula, we get the equation,
$$82000=\frac{X}{1.1}+\frac{3X}{1.21}$$
$$82000=\frac{1.1X}{1.21}+\frac{3X}{1.21}$$
$$82000=\frac{4.1X}{1.21}$$
$$X=24200$$
Total amount paid is 4X=96800
Interest paid is 96800-82000=14800
A sum of money is invested at a compound interest rate of 20% per annum, compounded annually. After 3 years, the amount becomes Rs. 8,640. If the same amount had been invested at a rate of 40% per annum, what would the new amount have been after 2 years?
Let the principal be Rs. X.
We have: $$8640=X\left(1.2\right)^3$$
Or, $$8640=1.728X$$
We get X = Rs. 5000
If Rs. 5000 is invested for 2 years at the rate of 40%,
Amount = $$5,000\times\ \left(1.4\right)^2$$
Rs. 9800
Educational materials for CAT preparation
91- 6303239042