Find the difference between the discount allowed on each 'X' and 'Y' type of article?

1. 5 Rs. 
2. 10 Rs.
3. 15 Rs.
4. 20 Rs.
5. 25 Rs. 

Explanation

- For article 'X':

- \( CP = \frac{8}{15} \times MP \).

- Profit % is 80% more than the discount %.

- Total revenue from 600 articles = 75,000 Rs, thus \( SP = \frac{75,000}{600} = 125 \) Rs.

- Calculate \( MP \) and \( Discount \) for 'X':

- Assume \( MP = m \).

- \( CP = \frac{8}{15}m \), and \( SP = 125 \).

- Profit = \( SP - CP \).

- Profit percentage on CP = Discount percentage + 80%.

- Solving gives: Discount allowed on each 'X' = 50 Rs.

- For article 'Y':

- \( CP = 0.7 \times MP \).

- Profit to discount ratio is 2:1.

- Total revenue from 700 articles = 126,000 Rs, thus \( SP = \frac{126,000}{700} = 180 \) Rs.

- Calculate \( MP \) and \( Discount \) for 'Y':

- Assume \( MP = n \).

- \( CP = 0.7n \), and \( SP = 180 \).

- Solving gives: Discount allowed on each 'Y' = 45 Rs.

- Difference in discount = 50 - 45 = 5 Rs.

Correct Answer: Option 1, 5 Rs.

Profit earned on each 'X' type of article is what percentage of the profit earned on each 'Y' type of article?

1. 100% 
2. 106.66% 
3. 112.5% 
4. 114.28%
5. 120%

Explanation

Let’s break this one down step by step, in plain English:

- Type X articles:

- Cost price : Marked price = 8 : 15 ? Let’s say cost is 8k, marked is 15k, k is some multiplier.

- Selling price is less than marked price (because discount), but you earn profit.

- Total revenue from 600 X = Rs. 75,000, so per article revenue (selling price) = 75,000 / 600 = Rs. 125.

- Type Y articles:

- Cost price is 70% of marked price. So, if marked is M, cost is 0.7M.

- Profit : Discount = 2 : 1.

- Total revenue from 700 Y = Rs. 1,26,000. So, per article revenue = 1,26,000 / 700 = Rs. 180.

For Type X:

- Let’s call cost price = 8k, marked price = 15k.

- Let selling price be S.

- So, profit = S - 8k, discount = 15k - S.

- The key line: Profit % = 80% more than discount %

- Discount % = (15k - S)/15k × 100%

- Profit % = (S - 8k)/8k × 100%

- Now, Profit % = Discount % + (80% of Discount %) = 1.8 × Discount %

- So, (S - 8k)/8k = 1.8 × (15k - S)/15k

- Solve this and you’ll get S in terms of k:

- (S - 8k)/8k = 1.8 × (15k - S)/15k

- Cross-multiply:

(S - 8k) × 15k = 1.8 × 8k × (15k - S)

15kS - 120k² = 14.4k(15k - S)

15kS - 120k² = 216k² - 14.4kS

15kS + 14.4kS = 216k² + 120k²

29.4kS = 336k²

S = (336/29.4)k = 11.43k

- But remember, selling price per piece = Rs. 125.

- So, 11.43k = 125 ? k ˜ 10.93

- So, cost price per piece = 8k ˜ 87.43, profit per piece = 125 - 87.43 = Rs. 37.57

For Type Y:

- Selling price per piece = Rs. 180.

- Let’s set marked price = M, cost = 0.7M, S = 180.

- Profit = S - 0.7M

- Discount = M - S

- Profit : Discount = 2 : 1

- So, S - 0.7M = 2 × (M - S)

- S - 0.7M = 2M - 2S

- S + 2S = 2M + 0.7M

- 3S = 2.7M

- S = 0.9M

- But S = 180 ? 0.9M = 180 ? M = 200

- Cost = 0.7 × 200 = 140

- Profit per article = 180 - 140 = Rs. 40

The main question:

What % is profit per X over profit per Y?

- Profit per X ˜ Rs. 37.57

- Profit per Y = Rs. 40

So, % = (37.57 / 40) × 100 = 93.93%

Here’s what it means:

- None of the options you listed matches 93.93%.

- Option 3 (112.5%) is not correct ()

Summary of key points:

- X type profit per article ˜ Rs. 37.57, Y type profit per article = Rs. 40

- Profit on X is 93.93% of that on Y

- None of the answer options are correct, but it’s definitely NOT 112.5%

So the closest, most honest answer I can give:

And here’s the breakdown you asked for, with the math to show why.

Find the ratio between the selling price of each 'X' type of article and the cost price of each 'Y' type of article?

1. 15 : 22 
2. 21 : 26 
3. 25 : 28 
4. 27 : 31 
5. 31 : 35

Explanation

Let’s break down the problem in a clear way:

For 'X' type:

- CP : MP = 8 : 15 ? If CP = 8x, then MP = 15x.

- Let discount = d, profit = p.

- Given p is 80% more than d ? p = 1.8d.

- SP = MP - discount = CP + profit ? 15x - d = 8x + p

? 15x - d = 8x + 1.8d ? 7x = 2.8d ? d = (7x/2.8) = 2.5x.

- So, discount = 2.5x, profit = 1.8 × 2.5x = 4.5x.

- SP = CP + profit = 8x + 4.5x = 12.5x.

- Total revenue from 600 articles: 75000 ?

SP (one X) = 75000/600 = 125. So, 12.5x = 125 ? x = 10.

- SP (X) = 125 rs.

For 'Y' type:

- CP = 70% of MP. Let MP = y, CP = 0.7y.

- Ratio profit : discount = 2 : 1 ? Let profit = 2k, discount = k.

- SP = MP - discount = y - k = CP + profit = 0.7y + 2k

? y - k = 0.7y + 2k ? 0.3y = 3k ? k = 0.1y.

- So, discount = 0.1y, profit = 0.2y.

- SP = CP + profit = 0.7y + 0.2y = 0.9y.

- Total revenue from 700 Y articles is 126000 ? SP (one Y) = 126000/700 = 180

So, 0.9y = 180 ? y = 200.

- CP (Y) = 0.7 × 200 = 140 rs.

Required Ratio:

- SP (X) : CP (Y) = 125 : 140 = 25 : 28.

Analysis of Options:

- 1) 15 : 22 ?

- 2) 21 : 26 ?

- 3) 25 : 28

- 4) 27 : 31 ?

- 5) 31 : 35 ?

Correct Answer:

- Option 3 (25 : 28)

If all articles of type 'X' had been sold without allowing any discount, then find the profit generated by selling all articles of type 'X'? 

1. 36000 Rs.
2. 38000 Rs.
3. 40000 Rs.
4. 42000 Rs
5. 44000 Rs.

Explanation

Correct option:4

Solution:-

For the 'X' type article, the cost price (CP) to marked price (MP) ratio is 8:15.

CP=8x  , MP=15x, SP=y

 Profit is 80% more than the discount.So the ratio of profit to discount=180:100=9:5

(y-8x)/(15x-y)=9/5
y=25/2 x
SP of 1 article=(25/2) x
SP of 600 article=600 * (25/2)x=75000
x=10
that means CP=80 ,SP=125, MP=150
it is given that If all articles of type 'X' had been sold without allowing any discount,
The profit generated by selling one articles of type 'X' =150-80=70
The profit generated by selling  all articles of type 'X' =70x600=42000
Hence 42000 is the correct answer.

Find profit earned from selling all articles of type 'Y'? 

1. 12000 Rs. 
2. 16000 Rs.
3. 20000 Rs. 
4. 24000 Rs. 
5. 28000 Rs. 

Explanation

Here’s the thing—let’s break it down step by step:

- For each 'Y' article, cost price = 70% of the marked price.

- Let’s call marked price 'M'. Cost price, CP = 0.7M.

- Profit to discount ratio for Y article: 2 : 1. Call profit ‘P’ and discount ‘D’. So, P = 2D.

- Selling price (SP) = Cost price + Profit = 0.7M + 2D

- Also, SP = Marked Price – Discount = M – D.

Set the two expressions for SP equal:

0.7M + 2D = M – D

0.7M + 3D = M

3D = 0.3M ? D = 0.1M

So, P = 2D = 0.2M.

Revenue from 700 articles = 126,000 Rs.

SP per article = 126,000 / 700 = 180 Rs.

Now, SP = M – D = M – 0.1M = 0.9M.

So, 0.9M = 180 ? M = 200.

Therefore, Discount D = 0.1M = 20

Profit per article P = 0.2M = 40

Profit from 700 articles = 40 × 700 = 28,000 Rs.

So, here’s the final check:

- Option 5, 28,000 Rs.  This is correct.

By: Parvesh Mehta