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- Question
- A merchant has 160 kgs of wheat. He sells a part of it at 10% profit and the rest of 6% loss. If he incurs 4% loss on the whole, find the quantity for each part.
Options- A. 120 kgs
- B. 140 kgs
- C. 150 kgs
- D. 160 kgs
- Correct Answer
- 140 kgs
ExplanationAccording to figure we can find that the ration would be 1 : 7.
Quantity sold at 10% profit = 1 / (1 + 7)× 160 = 20 kgs.
Quantity sold at 6% loss = (160 ? 20) = 140 kgs. - 1. A person has two solutions of sugar with 30% and 50% concentration respectively. In what proportion should he mix two solutions to get 45% concentration in the resulting mixture?
Options- A. 1 : 3
- B. 3 : 1
- C. 2 : 3
- D. 3 : 2 Discuss
- 2. Find the quantity of rice @ Rs. 10 per kg. which should be mixed with 25 kgs of rice @ Rs. 8 per kg, so that on selling the mixture @ Rs. 15 per kg there is 80% profit.
Options- A. 6 kgs
- B. 7 kgs
- C. 3 kgs
- D. 5 kgs Discuss
- 3. In what proportion must tea at Rs. 62 per kg be mixed with tea at Rs. 72 per kg in order to obtain the mixture worth Rs. 65 per kg?
Options- A. 4: 6
- B. 7: 3
- C. 2: 3
- D. 4: 7 Discuss
- 4. Two solution of 90% and 97% purity and mixed resulting in 21 liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
Options- A. 15 litres
- B. 12 litres
- C. 9 litres
- D. 6 litres Discuss
- 5. In what ratio should milk and water be mixed so that after selling the mixture at the cost price a profit of 50/3 % is made?
Options- A. 1:2
- B. 6:1
- C. 2:3
- D. 2:5 Discuss
- 6. A man bought a certain quantity of sugar for Rs. 8000. He sells one-fourth of it at 20% loss. At what per cent profit should he sell the remainder stock so as to make an overall profit of 20%?
Options- A. 20%
- B. 30%
- C. 35%
- D. 40% Discuss
- 7. A person has Rs. 5000. He invests a part of it at 3% per annum and the remainder at 8% per annum simple interest. His total income in 3 years is Rs. 750. Find the sum invested at different rates of interest.
Options- A. Rs. 2000 and Rs. 3000
- B. Rs. 2500 and Rs. 2500
- C. Rs. 3000 and Rs. 2000
- D. Rs. 2750 and Rs. 2250 Discuss
- 8. The average daily wages of staff, consisting of supervisors and labourers, of a company is Rs. 50. The average wages of supervisors is Rs. 150 while that of labourers is Rs. 40 per day. If the number of supervisors is 15, find the number of labourers in the company.
Options- A. 150
- B. 175
- C. 180
- D. 200 Discuss
- 9. A sum of Rs. 70 is divided among 10 children. Each boy gets Rs. 10 whereas a girl gets Rs. 5. If the number of boys is 4, find the number of girls.
Options- A. 6
- B. 7
- C. 8
- D. 9 Discuss
- 10. A vessel contains 80 litres of milk. 16 litres of milk was taken out of the vessel and replaced by water. Then 16 litres of mixture was withdrawn and again replaced by water. The operation was repeated for third time. How much milk is now left in the vessel?
Options- A. 96.40 litres
- B. 50.36 litres
- C. 40.96 litres
- D. 32.76 litres Discuss
Alligation or Mixture problems
Search Results
Correct Answer: 1 : 3
Explanation:
He should mix 30% and 50% in the ratio 5 : 15 or 1 : 3.
( 30% Solution ) / (50% Solution) = 1 / 3 or 1 : 3
Correct Answer: 5 kgs
Explanation:
Cost price of the mixture = 15 × (100 / 180) = Rs. 25/3 per kg
(Quantity of rice @ Rs. 8 per kg) / (Quantity of rice @ Rs.10 per kg) = (5 / 3) / (1/3) = 1/5
Quantity of rice @ Rs. 10 per kg = 25 × (1/ 5) = 5 kgs.
Correct Answer: 7: 3
Explanation:
Using Alligation rule,
(Quantity of cheaper tea) / (Quantity of dearer tea) = (d - m) / (m - c) = 7/3
Therefore, they must be mixed in the ratio of 7 : 3.
Correct Answer: 9 litres
Explanation:
Method 1 to solve the equation.
Let us assume the number of liters of the 90% purity solution = A
and the number of liters of the 97% purity solution = B.
According to question,
Since there are 21 liters of the solution,
A + B = 21 ...................... (1)
Since after mixing the two solutions the new mixture has 94% purity,
Concentrate of A + Concentrate of B = Concentrate of (A + B)
A x 90% + B x 94% = (A+ B) x 97%
? A x 90/100 + B x 97/100 = (A + B) x 94/100
? 90A + 97B = (A + B) x 94
? 90A + 97B = 94A + 94B
? 94A + 94B - 90A- 97B = 0
? 4A - 3B = 0 ........................(2)
Multiply the 3 with Equation (1) and add with Equation (2),
3A + 3B + 4A - 3B = 63 + 0
? 7A = 63
? A = 63/7 = 9
Put the value of A in Equation (1) , we will get
9 + B = 21
B = 21 - 9
B = 12
The first solution would be A = 9 liters.
Method 2 to solve the equation.
Hit and trail method.
94% is closer to 97% but barely meaning the mixtures will not be equal parts but will be slightly more of the higher purity. Quickly eliminate A and B. Out of the others 9 is the easy choice. If the other choices were closer to half this wouldn't work.
Correct Answer: 6:1
Explanation:
Method 1 to solve the equation.
Let us assume Cost Price (C.P) of 1 liter milk be Y rupees.
According to question,
Selling Price (S.P) of 1 liter of mixture Y rupees. (Selling price should be same as Cost price)
Profit = 50/3 %
Let us assume Cost price of 1 Liter of Mixture of Water and Milk = C
Cost price of 1 Liter of Mixture of Water and Milk = Selling price of Mixture - Profit
C = Y - C x 50/3%
? C = Y - C x 50/3x100
? C = Y - C x 1/3x2
? C = Y - C/6
? Y = C + C/6
? Y = (6C + C)/6
? Y = (6C + C)/6
? Y = 7C/6
? C = 6Y/7
Since in Y rupees we will get 1 liter milk.
Hence in 1 rupees we will get 1/Y liter milk.
Hence in 6Y/7 rupees we will get 1 x 6Y/7 x Y liter milk.
Hence in 6Y/7 rupees we will get 6/7 liter milk.
We need 1 liter mixture of milk and water for sold on the same price, we need to mix the water.
So water quantity in mixture = 1 - 6/7 = 1/7
Ratio of Milk and water in mixture = quantity of Milk in Mixture/quantity of Water in Mixture
Ratio of Milk and water in mixture = 6/7 / 1/7
Ratio of Milk and water in mixture = 6 x 7 / 7
Ratio of Milk and water in mixture = 6 / 1
Ratio of Milk and water in mixture = 6 : 1
Method 2 to solve the question.
Let the original amount of milk be 1 liter and the cost price is 1 rupees per liter.
Cost price of milk = 1 rupees.
Selling price of Mixture = 1 rupees.
When the milk is mix with x liters of water milk remaining is 1- x.
Let us assume the cost price of milk in mixture is Y and given that the Sold Price is 1.
we should use the Profit formula in algebra,
Y + Y x 50/3 % = 1
Y + Y x 50/3 x 100 = 1
Y + Y x /3 x 2 = 1
7Y/6 = 1
Y = 6/7
Y = 6/7 is the cost price of Mixture for 1 liter.
Since water is free so there is not cost of water in mixture. So price of milk is 6/7 rs in mixture.
Since as per question,
In 1 rupees we will get 1 liter of milk.
hence in 6/7 rupees we will get 1 x 6/7 = 6/7 liter of milk.
Now we have to make 1 liter of mixture with water and milk.
quantity of Water + Quantity of Milk = 1 liter
quantity of Water + 6/7 = 1
quantity of Water = 1 - 6/7 = (7 - 6)/7
quantity of Water = 1/7
Ratio of milk and Water = Quantity of Milk / quantity of Water
Ratio of milk and Water = (6/7) / (1/7)
Ratio of milk and Water = (6/7) x (7/1)
Ratio of milk and Water = 6 x 7/ 7 x 1
Ratio of milk and Water = 6 :1
Correct Answer: 30%
Explanation:
Let the remainder stock be sold at P% profit.
(P - 20) / 30 = ((1 / 4) / (3 / 4))
or (P ? 20) = 30 × (1 / 3)
or P = 20 + 10
P = 30% profit.
Correct Answer: Rs. 3000 and Rs. 2000
Explanation:
Average rate of interest = (100 * 750) / (5000 * 3) = 5% per annual
Investment at 3% per annual = 3 / (3 + 2) × 5000 = Rs. 3000 Investment at 8% per annual = 2 / (3 + 2) × 5000 = Rs. 2000
Correct Answer: 150
Explanation:
As per figure we can calculate the ration as below.
Number of supervisors / Number of labourers = (10 / 100) = 1/10
Total number of labourers = Total no. of supervisors × 10
= 15 × 10 = 150.
Correct Answer: 6
Explanation:
Number of girls / Number of boys = (3 / 2)
Number of girls = (3 / 2) × 4 = 6
Correct Answer: 40.96 litres
Explanation:
Amount of milk left = 80 [1 - (16 / 80)]3 = 80 (4 / 5)3
80 × (64 / 125) = 40.96 liters.
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