A mixture contains 15 kg of rice at Rs. 60 per kg and 25 kg of rice at X per kg are mixed and sold at Rs.97.5 per kg. The profit earned by the seller is 30%. What will be the value of x?Question 15Answera.72b.84c.80d.77
Question
A mixture contains 15 kg of rice at Rs. 60 per kg and 25 kg of rice at X per kg are mixed and sold at Rs.97.5 per kg. The profit earned by the seller is 30%. What will be the value of x?Question 15Answera.72b.84c.80d.77
Solution 1
To find the value of X, we need to follow these steps:
Step 1: Calculate the cost price of the total mixture.
The cost price of the 15 kg rice at Rs. 60 per kg is 15 kg * Rs. 60/kg = Rs. 900.
The cost price of the 25 kg rice at X per kg is 25 kg * X = 25X.
So, the total cost price of the mixture is Rs. 900 + 25X.
Step 2: Calculate the selling price of the mixture.
The mixture is sold at Rs. 97.5 per kg. So, the total selling price for the 40 kg mixture (15 kg + 25 kg) is 40 kg * Rs. 97.5/kg = Rs. 3900.
Step 3: Calculate the profit.
The profit earned by the seller is 30%. So, the cost price of the mixture is 70% of the selling price (because 100% - 30% = 70%).
So, 900 + 25X = 70/100 * 3900.
Solving this equation will give us the value of X.
900 + 25X = 2730,
25X = 2730 - 900,
25X = 1830,
X = 1830 / 25,
X = Rs. 73.2.
So, the value of X is closest to 72 (option a).
Solution 2
To find the value of X, we need to follow these steps:
Step 1: Calculate the cost price of the total mixture.
The cost price of the 15 kg rice at Rs. 60 per kg is 15*60 = Rs. 900.
Let's assume the cost price of the 25 kg rice is X per kg. So, the total cost price for this is 25*X.
Therefore, the total cost price of the mixture is 900 + 25X.
Step 2: Calculate the selling price of the mixture.
The mixture is sold at Rs. 97.5 per kg. So, the total selling price for the 40 kg (15 kg + 25 kg) mixture is 40*97.5 = Rs. 3900.
Step 3: Calculate the cost price based on the profit percentage.
The seller earns a profit of 30%. This means the selling price is 130% of the cost price. So, we can set up the equation:
130/100 * (900 + 25X) = 3900
Solving this equation will give us the value of X.
Step 4: Solve the equation.
130*(900 + 25X) = 3900*100
117000 + 3250X = 390000
3250X = 390000 - 117000
3250X = 273000
X = 273000 / 3250
X = 84
So, the value of X is 84. Therefore, the cost price of the 25 kg rice is Rs. 84 per kg. The correct answer is (b) 84.
Similar Questions
Select the correct answerA trader mixes 30kg of rice at Rs 25 per kg with 20kg of rice of other variety at Rs 40 per kg and sells the mixture at Rs 35 per kg. Find the profit percent?Options12.90%11%13.67%17%
A farmer mixes two varieties of rice of price Rs. 36 per kg and Rs. 24 per kg in the ratio of 1: 2, respectively. He sold the mixture for Rs. 2100 to earn a profit of 25%, then find the quantity of rice of cost Rs. 24 per kg used in the mixture. 20 kg30 kg40 kg50 kg60 kg
7. A shopkeeper purchased two varieties of rice, 80 KG at Rs. 13.50 per KG and 120 KG at Rs. 16 per KG. The shopkeeper being greedy, mixed the two varieties of rice and sold the mixture at a gain of 16 %. Find the per KG selling price of the mixture.*Rs. 17.40Rs 20Rs 25Rs 11
10 kg Rice was bought at the rate of the of Rs.10/kg and 15 kg Rice was bought at the rate of Rs.12/kg. Find the % profit / loss, if the total rice is sold for Rs.16/kgQuestion 13Answera.35b.42.86c.40d.57.28
A shop keeper bought 30 kg. of wheat at the rate of Rs.45 per kg. He sold 40% of the total quantity at the rate of Rs.50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make 25% overall profit?a.Rs.56b.Rs.50c.Rs.60d.Rs.54
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.