Question

By producing two sharis, Rama aunti sold one shari at 15% profit and another at 20% profit. She has made total profit by 262.50. If the ratios of production costs of two sharee1-3 what will be the production cost of each of the two saree?​

Answer 1

Let :-

• The cost price of 1st saree = S
• The cost price of 2nd saree = M

Given :-

• The ratio of cost 1st and 2nd saree = 1 : 3

To Find :-

• The cost price of each saree = ?

Solution :-

• To calculate the cost price of each saree at first we have to set up equation by applying formula with the help of given clue in the question.

Calculation for 1st equation :-

• CP (1st saree) = S. P = 15%
• CP (2nd saree) = M P = 20%

⇒ SP = (100 + P%/100) × CP

⇒ Total SP = Total CP + Profit

⇒ (100 + 15/100) × S + (100 + 20/100) × M = S + M + 262.50

⇒ 115S/100 + 120M/100 = S + M + 262.5

⇒ 115S + 120M/100 = S + M + 262.5

⇒ 115S + 120M = 100S + 100M + 26250

⇒ 115S - 100S + 120M - 100M = 26250

⇒ 15S + 20M = 26250--------(i)

Calculation for 2nd equation :-

• The ratio of cost two saree = 1 : 3

⇒CP of 1st saree : CP of 2nd saree = 1:3

⇒S/M = 1/3

⇒ 3S = M --------(ii)

• Substituting the value of M in eq (i) :-]

⇒ 15S + 20M = 26250

⇒ 15S + 20(3S) = 26250

⇒ 15S + 60S = 26250

⇒ 75S = 26250

⇒ S = 350

• Putting the value of S in eq (I) :-]

⇒ 15S + 20M = 26250

⇒ 15(350) + 20M = 26250

⇒ 20M + 5250 = 26250

⇒ 20M = 26250 - 5250

⇒ 20M = 21000

⇒ M = 1050

Hence,

• The cost price of 1st saree (S) = 350
• The cost price of 2nd saree (M) = 1050

Answer 2

Question:

• By producing two sarees, Rama aunty sold one saree at 15% profit and another at 20% profit. She has made total profit by Rs. 262.50. If the ratio of production costs of two sarees is 1:3 what will be the production cost of each of the two saree?

Answer:

• Production costs of each of the two sarees are Rs. 350 and Rs. 1050.

Explanation:

Given that:

• Profit on first saree = 15%
• Profit on second saree = 20%
• Ratio of production costs of two sarees is 1:3

To Find:

• Production costs (CP) of each of the two sarees?

Solution:

• It is given that ratio of production costs of two sarees is 1:3. So, let the production cost of 1st saree be x and production cost of 2nd saree be 3x.

We know that,

⧪ 1st saree makes 15% profit on CP ⧪

Therefore,

➼ $\sf Profit = \dfrac{15}{100}\:\times\:x$

➼ $\sf Profit = \dfrac{15\:\times\:x}{100}$

➼ $\bf \pink{Profit = \dfrac{15x}{100}} \quad- - - (1)$

Again we know that,

⧪ 2nd saree makes 20% profit on CP ⧪

Therefore,

➼ $\sf Profit = \dfrac{20}{100}\:\times\:3x$

➼ $\sf Profit = \dfrac{20\:\times\:3x}{100}$

➼ $\bf \purple{Profit = \dfrac{60x}{100}} \quad- - - (2)$

• Now, calculating total profit ::

➼ $\sf Total\:profit = (1) + (2)$

➼ $\sf Total\:profit = \dfrac{15x}{100} + \dfrac{60x}{100}$

➼ $\sf Total\:profit = \dfrac{15x + 60x}{100}$

➼ $\sf Total\:profit = \dfrac{\cancel{75}x}{\cancel{100}}$

➼ $\bf \green{Total\:profit = \dfrac{3x}{4}}$

• Also, total profit is given to us i.e, total profit = 262.50.

Therefore,

➼ $\sf Total\:profit = \dfrac{3x}{4} = 262.50$

➼ $\sf \dfrac{3x}{4} = 262.5$

➼ $\sf 3x = 262.5\:\times\:4$

➼ $\sf 3x = 1050$

➼ $\sf x = {\cancel{\dfrac{1050}{3}}}$

➼ $\bf \red{x = 350}$

Hence,

➻ CP of first saree = x

➻ CP of first saree = Rs. 350

Also,

➻ CP of second saree = 3x

➻ CP of second saree = 3 × 350

➻ CP of second saree = Rs. 1050

∴ Production costs of each of the two sarees are Rs. 350 and Rs. 1050.

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