A utilities company sells electrical wiring at $7 per 15 meters, which

Question

A utilities company sells electrical wiring at $7 per 15 meters, which costs them around $3 per 15 meters to make. If a customer purchases at least 300 meters, the company offers a 10% discount on the rate, with the discount given increasing by 5% for each additional 300 meters, such that 600 meters would receive a 15% discount on the total bill. They must sell less than what length of wire if they wish to have at least a 40% profit margin?

(A) 600 meters
(B) 900 meters
(C) 1200 meters
(D) 1500 meters
(E) 1800 meters

(A) 600 meters
(B) 900 meters
(C) 1200 meters
(D) 1500 meters
(E) 1800 meters

siddhantvarma · Answer

Selling Price: $7 / 15 meters = $0.4667 per meter
Cost Price: $3 / 15 meters = $0.2 per meter

For 300-599 meters (10% discount):
Price after discount: $0.4667 * 0.9 = $0.42 per meter
Profit per meter: $0.42 - $0.2 = $0.22
Profit margin: ($0.22 / $0.42) * 100 = 52.38%

For 600-899 meters (15% discount):
Price after discount: $0.4667 * 0.85 = $0.3967 per meter
Profit per meter: $0.3967 - $0.2 = $0.1967
Profit margin: ($0.1967 / $0.3967) * 100 = 49.58%

For 900-1199 meters (20% discount):
Price after discount: $0.4667 * 0.8 = $0.3734 per meter
Profit per meter: $0.3734 - $0.2 = $0.1734
Profit margin: ($0.1734 / $0.3734) * 100 = 46.44%

For 1200-1499 meters (25% discount):
Price after discount: $0.4667 * 0.75 = $0.35 per meter
Profit per meter: $0.35 - $0.2 = $0.15
Profit margin: ($0.15 / $0.35) * 100 = 42.86%

For 1500-1799 meters (30% discount):
Price after discount: $0.4667 * 0.7 = $0.3267 per meter
Profit per meter: $0.3267 - $0.2 = $0.1267
Profit margin: ($0.1267 / $0.3267) * 100 = 38.78%

We can see that the profit margin drops below 40% when the length reaches 1500 meters.
  Therefore, the correct answer is (D) 1500 meters. They must sell less than 1500 meters of wire to maintain at least a 40% profit margin.

This definitely took me a while, hopefully someone has a more time-efficient way of solving this question.

Yoaerez · Answer

siddhantvarma  I'll have a crack at it, tell me what you think:

So X is the amount of 15 meter wire the company bought, they paid 3x for it

They sell each 15 meters for $7, so they sell the first 20x (300 meters) for 0.9*7*20 = 126, and they paid 60 for it. You can instinctively tell that it's above 40%.

With these questions I always plug in the middle answer and check if it's higher or lower:

1200 meters = 80x.

300 = 0.9 of the original price
600 = 0.85
900 = 0.8
1200 = 0.75 = 3/4

so calculate 80*(3/4)*7 = $420, and it cost the company $240. 24/42 = ≈0.57, or 1-0.57 = 0.43*100 = ≈43% profit margin.

This means that D, 1500, will probably be a bit less than 40% margin, but we can check anyway:

1500 = 0.7*100*7 = $490, and it cost the company 3*100 = $300. 300/490 = 60/98, which again intuitively means that it's a bit more than 60/100. 1-(61/100) = 39% margin, which is below the 40% margin that the company wants.

Thus, the company can sell more than 1200 but less than 1500. Answer  D

With this sort of questions I estimate a lot so let me know if this method is not correct.

sayan640 · Answer

KarishmaB   MartyMurray  Any quick method to solve this one ? Kindly help.

Kinshook · Answer

Bunuel Please check the OA and tell me where I am wrong.

Given: A utilities company sells electrical wiring at $7 per 15 meters, which costs them around $3 per 15 meters to make. If a customer purchases at least 300 meters, the company offers a 10% discount on the rate, with the discount given increasing by 5% for each additional 300 meters, such that 600 meters would receive a 15% discount on the total bill.

Asked: They must sell less than what length of wire if they wish to have at least a 40% profit margin?

For at least 40% profit margin, selling price > 3*1.4 = $4.2 per 15 meters
If Discount possible is D%, selling price = 7(1-D%/100) > 4.2
1 - D%/100 > 4.2/7 = .6
D% < 40%

10% + 5%(x-300)/300 < 40%
x - 300 < 6*300 ; x < 2100 meters
They must sell less than 300 + 6*300 = 2100 meters length of wire.

IMO E

Kinshook · Answer

sayan640   Bunuel

Please check my revised solution. 
Bunuel is requrested to revise OA if needed.

sayan640 
Please delete this comment since I have taken min 50% profit margin instead of 40%.

sayan640 · Answer

I think your mistake is in the highlighted part. The answer is D indeed.

MartyMurray · Answer

A utilities company sells electrical wiring at $7 per 15 meters, which costs them around $3 per 15 meters to make. If a customer purchases at least 300 meters, the company offers a 10% discount on the rate, with the discount given increasing by 5% for each additional 300 meters, such that 600 meters would receive a 15% discount on the total bill. They must sell less than what length of wire if they wish to have at least a 40% profit margin?

(A) 600 meters
(B) 900 meters
(C) 1200 meters
(D) 1500 meters
(E) 1800 meters

The current price is $7.

Profit Margin  = \frac{Price - Cost}{Price}

So, the price after discounts, p, at which the profit margin will be at least 40% will be such that  \frac{p - 3}{p} = 0.40 .

Solve for the mininum price p:

\frac{p - 3}{p} = 0.40

p - 3 = 0.40p

0.60p = 3

p = 5

So, the minimum price at which they can make a 40% margin is $5.

$7 - $5 = $2

So, we can discount the price a max of $2.

$2/$7 ≈ 29%

So, we can discount the price a max of 29%.

10% + (3 * 5%) = 25%

10% + (4 * 5%) = 30%

So, the price must be discounted a max of 4 times, meaning under 5 times.

300 * 5 = 1500

(A) 600 meters

(B) 900 meters

(C) 1200 meters

(D) 1500 meters

(E) 1800 meters

Correct answer:  D

KarishmaB · Answer

CP = $3
Marked Price = $7
Profit Margin (calculated on SP) required is at least = 40%

CP + Profit = SP
$3 + 40% of S = S
which gives S = $5

Hence the selling price can fall to at most $5 which means that the maximum discount that can be given =  \frac{2}{7} = 29%  (Recall 1/7 = 14.28%)

This means that we cannot give a 30% discount. The discount should not reach (10% + 4*5%).
So the length of the wire should not reach (300 + 4*300) = 1500 meters

Answer (D)

aksjain2401 · Answer

Marked price per 15 m = $7, cost per 15 m = $3.

Profit margin = (selling price − cost) / selling price. For a discount d selling price per 15 m is 
7(1−d).

Require

/ {7(1−d)} ≥ 0.40

1 −  ≥ 0.4

1-0.4 ≥

0.6 ≥

7(1−d) ≥ 3/0.6

7(1−d) ≥ 5

1−d ≥ 5/7

2/7 ≈ 28.57%.

300 m → 10%, 600 m → 15%, 900 m → 20%, 1200 m → 25%, 1500 m → 30%.

Hence , <1500m, so Option D.

A utilities company sells electrical wiring at $7 per 15 meters, which

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A utilities company sells electrical wiring at $7 per 15 meters, which

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