55749.Rakesh bought 20 chairs for Rs.1000. He repaired and sold them at the rate of Rs.500 per pair. He got profit of Rs.100 per chair. How much did he spend on repairs?
Rs.1500
Rs.2000
Rs.2500
Rs.1800
Explanation:
Purchase price for 20 chairs=Rs. 1000
Repairs amount (to be determined) =Rs. X
Sales price for 20 chairs = Rs. 5000
Profit derived for 20 chairs = Rs. 2000
We have, (3) - [(1) + (2)] = (4).
? 5000 - (1000 + X) = 2000 => X = 2000
Purchase price for 20 chairs=Rs. 1000
Repairs amount (to be determined) =Rs. X
Sales price for 20 chairs = Rs. 5000
Profit derived for 20 chairs = Rs. 2000
We have, (3) - [(1) + (2)] = (4).
? 5000 - (1000 + X) = 2000 => X = 2000
55750.There were three partners, A, B, C in a business, and each had a share of the profits in proportion to his capital. A’s capital was Rs.240; B’s Rs.640; and A’ share was Rs.15 in every Rs.100. Find B’s share of profits and C’s capital.
Rs.30 in every Rs.100; Rs.750
Rs.60 in every Rs.100; Rs.700
Rs.50 in every Rs.100; Rs.800
Rs.40 in every Rs.100; Rs.720
Explanation:
A’s share of capital = Rs.15 in every Rs.100
⇒ A’s share = (15/100) × (Total Capital)
⇒ Total capital = (100/15) × A’s share = (100/15) × 240 = Rs.1600
∴ C’s capital = (1600 – 240 – 640) = Rs.720
B’s share of capital = Say Rs.X in every Rs.100
⇒ 640 = (X/100) × 1600
⇒ X = (640/1600) × 100 = Rs.40 in every Rs.100
A’s share of capital = Rs.15 in every Rs.100
⇒ A’s share = (15/100) × (Total Capital)
⇒ Total capital = (100/15) × A’s share = (100/15) × 240 = Rs.1600
∴ C’s capital = (1600 – 240 – 640) = Rs.720
B’s share of capital = Say Rs.X in every Rs.100
⇒ 640 = (X/100) × 1600
⇒ X = (640/1600) × 100 = Rs.40 in every Rs.100
55751.The marked price of a Pant and a T-Shirt are in the ratio of 2 : 3. The shopkeeper gives 40% discount on the Pant. If the total discount on the Pant and the T-Shirt is 40% the discount offered on the T-Shirt is
28 $\dfrac{1}{3}$%
18 $\dfrac{2}{3}$%
26 $\dfrac{2}{3}$%
None of these
Explanation:
Let the marked price of the pant be Rs. 200.
Then marked price of T-Shirt will be Rs. 300.
Discounted price of Pant = 200 × 60/100 = Rs. 120
Let the discounted price of T- Shirt be x.
According to the question,
120 + x = 60/100× (200 + 300)
or, 120 + x = 300
or, x = 180
Discounted offered on the T - Shirt
= 300 – 180/300 × 100 = 40%
Note: If overall discount is 40% and discount on one part is also 40% then naturally the discount on the second part is also 40%.
Let the marked price of the pant be Rs. 200.
Then marked price of T-Shirt will be Rs. 300.
Discounted price of Pant = 200 × 60/100 = Rs. 120
Let the discounted price of T- Shirt be x.
According to the question,
120 + x = 60/100× (200 + 300)
or, 120 + x = 300
or, x = 180
Discounted offered on the T - Shirt
= 300 – 180/300 × 100 = 40%
Note: If overall discount is 40% and discount on one part is also 40% then naturally the discount on the second part is also 40%.
55753.A, B and C participated in a burger eating competition. A beat C by 18 burgers. A also beat B by eating 50% more burger than B. Also B had eaten 5 percentage points more burger than C. Find the overall number of burgers that were eaten.
90 burgers
81 burgers
72 burgers
100 burgers
Explanation:
Let the burgers eaten by C be x%
=> Burgers eaten by B = x + 5%
Since A ate 50% more than B = (x + 5%) + 50% of (x+5%) = 1.5 (x+5%)
=> x + x + 5 + 1.5(x+ 5) = 100%
=> x = 87.5/3.5 = 25
Therefore, A beat C by 20 percentage points => 18 => Total burger = 18 * 100/20= 90
The question is " Find the overall number of burgers that were eaten. "
The overall number of burgers that were eaten is 90.
Hence, the answer is 90
Let the burgers eaten by C be x%
=> Burgers eaten by B = x + 5%
Since A ate 50% more than B = (x + 5%) + 50% of (x+5%) = 1.5 (x+5%)
=> x + x + 5 + 1.5(x+ 5) = 100%
=> x = 87.5/3.5 = 25
Therefore, A beat C by 20 percentage points => 18 => Total burger = 18 * 100/20= 90
The question is " Find the overall number of burgers that were eaten. "
The overall number of burgers that were eaten is 90.
Hence, the answer is 90
55754.Rahim marks up all Jeans in his shop 20% higher. He gave 25% discount on 2/5th of the total Jeans and 12% discount on 1/4th of the total Jeans. If Rahim gets an overall profit of 2.3%, then what percentage of discount should be given by Rahim to customers on the remaining Jeans.
5%
15%
17%
6%
Explanation:
Let Rahim has 100 Jeans and C.P of each Jeans is Rs. 100.
Then, Marked price of each Jeans = 100 × 120/100 = Rs. 120
And, Selling price of 100 Jeans = 100 × 100 × 102.3/100 = Rs. 10230
Selling price of 40 Jeans (i.e., 2/5 of 100) = 40 × 120 ×75/100 = 3600
Selling price of 25 Jeans (i.e., 1/4 of 100) = 25 × 120 ×88/100 = 2640
Let Rahim gave a% discount on remaining (i.e., 100 – 40 – 25 = 35) Jeans.
Selling price of remaining 35 Jeans
= 35 × 120 ×100 – a/100 = 4200 ×100 – a /100
According to the question,
10230 = 3600 + 2640 + 4200 ×100 – a/100
⇒ 4200 ×100 – a /100 = 10230 – 6240 = 3990
⇒ 100 – a/100 = 3990 /4200 = 0.95
⇒ 100 – a = 95
⇒ a = 100 – 95
⇒ a = 5%
Let Rahim has 100 Jeans and C.P of each Jeans is Rs. 100.
Then, Marked price of each Jeans = 100 × 120/100 = Rs. 120
And, Selling price of 100 Jeans = 100 × 100 × 102.3/100 = Rs. 10230
Selling price of 40 Jeans (i.e., 2/5 of 100) = 40 × 120 ×75/100 = 3600
Selling price of 25 Jeans (i.e., 1/4 of 100) = 25 × 120 ×88/100 = 2640
Let Rahim gave a% discount on remaining (i.e., 100 – 40 – 25 = 35) Jeans.
Selling price of remaining 35 Jeans
= 35 × 120 ×100 – a/100 = 4200 ×100 – a /100
According to the question,
10230 = 3600 + 2640 + 4200 ×100 – a/100
⇒ 4200 ×100 – a /100 = 10230 – 6240 = 3990
⇒ 100 – a/100 = 3990 /4200 = 0.95
⇒ 100 – a = 95
⇒ a = 100 – 95
⇒ a = 5%
55755.A shopkeeper gives 25% discount on an article and makes a profit of 10%. If the cost price of the article is Rs 300 then what is the marked price?
Rs 360
Rs 480
Rs 404
Rs 440
Explanation:
Relationship between CP and MP
CP : MP = (100 – D%) : (100 + P%)
CP : MP = (100 – 25) : (100 + 10) = 75 : 110 = 15 : 22
now, CP = 15 units = 300
So MP = 22 units = Rs. 440
Relationship between CP and MP
CP : MP = (100 – D%) : (100 + P%)
CP : MP = (100 – 25) : (100 + 10) = 75 : 110 = 15 : 22
now, CP = 15 units = 300
So MP = 22 units = Rs. 440
55756.Vivek bought 5 dozen apples at the rate of Rs.15 per dozen. He spent Rs.15 on transportation. If he sold the apples at the rate of Rs.24 per dozen, what was his profit percentage?
25%
30%
33.33%
60%
Explanation:
The Cost Price (C.P) of 1 dozen apples = Rs.15.
Hence, the C.P of 5 dozen apples = 15 x 5 = Rs.75.
Adding Rs.15 towards transportation cost, the total cost price of 5 dozen apples becomes Rs.90.
Now, the Selling Price (S.P) of 1 dozen apples = Rs.24.
Hence, the Sales Revenue of 5 dozen apples = 24 x 5 = Rs.120.
Thus, Net Profit = Sales Revenue - Cost Price = 120 - 90 = Rs.30.
The Profit is always expressed as a percentage to cost price. Required answer = (30/90) x 100 = 33.33%. Ans.(3)
Short-cut: Cost of 5 dozen of apples including transportation charges = 15 + (15/3) = Rs.18.
Percentage profit = [(24-18)/18] x100=33.33% .
The Cost Price (C.P) of 1 dozen apples = Rs.15.
Hence, the C.P of 5 dozen apples = 15 x 5 = Rs.75.
Adding Rs.15 towards transportation cost, the total cost price of 5 dozen apples becomes Rs.90.
Now, the Selling Price (S.P) of 1 dozen apples = Rs.24.
Hence, the Sales Revenue of 5 dozen apples = 24 x 5 = Rs.120.
Thus, Net Profit = Sales Revenue - Cost Price = 120 - 90 = Rs.30.
The Profit is always expressed as a percentage to cost price. Required answer = (30/90) x 100 = 33.33%. Ans.(3)
Short-cut: Cost of 5 dozen of apples including transportation charges = 15 + (15/3) = Rs.18.
Percentage profit = [(24-18)/18] x100=33.33% .
55757.A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
Rs. 2160
Rs. 1420
Rs. 1580
Rs. 2210
Explanation:
CP = 80 × 40
Profit from the n objects = n% × 40 × n.
Profit from the remaining objects = (100 – n)% × 40 × (80 – n).
We need to find the minimum possible value of n% × 40 × n + (100 – n)% × 40 × (80 – n).
Or, we need to find the minimum possible value of n^2 + (100 – n) (80 – n).
Minimum of n^2 + n^2 – 180n + 8000
Minimum of n^2 – 90n + 4000
Minimum of n^2 – 90n + 2025 – 2025 + 4000
We add and subtract 2025 to this expression in order to crate an expression that can be expressed as a perfect square.
Minimum of n^2 – 90n + 2025 + 1975 = (n – 45)^2 + 1975
This reaches minimum when n = 45.
When n = 45, the minimum profit made
45% × 40 × 45 + 55% × 40 × 35
18 × 45 + 22 × 35 = 810 + 770 = 1580
The question is "What is the minimum profit the merchant could have made on this trade?"
Hence, the answer is Rs. 1580.
CP = 80 × 40
Profit from the n objects = n% × 40 × n.
Profit from the remaining objects = (100 – n)% × 40 × (80 – n).
We need to find the minimum possible value of n% × 40 × n + (100 – n)% × 40 × (80 – n).
Or, we need to find the minimum possible value of n^2 + (100 – n) (80 – n).
Minimum of n^2 + n^2 – 180n + 8000
Minimum of n^2 – 90n + 4000
Minimum of n^2 – 90n + 2025 – 2025 + 4000
We add and subtract 2025 to this expression in order to crate an expression that can be expressed as a perfect square.
Minimum of n^2 – 90n + 2025 + 1975 = (n – 45)^2 + 1975
This reaches minimum when n = 45.
When n = 45, the minimum profit made
45% × 40 × 45 + 55% × 40 × 35
18 × 45 + 22 × 35 = 810 + 770 = 1580
The question is "What is the minimum profit the merchant could have made on this trade?"
Hence, the answer is Rs. 1580.
55758.A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
24
18
27
32
Explanation:
Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n2 + n ≥ 28n
n2 - 27n ≥ 0
n ≥ 27
The question is " If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?"
He should sell a minimum of 27 goods.
Hence, the answer is 27.
Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n2 + n ≥ 28n
n2 - 27n ≥ 0
n ≥ 27
The question is " If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?"
He should sell a minimum of 27 goods.
Hence, the answer is 27.