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- Question
In what ratio should two varieties of sugar at Rs.18 per kg and Rs.24 Kg be mixed together to get a mixture whose cost is Rs.20 per kg?
Options- A. 1:3
- B. 3:1
- C. 1:2
- D. 2:1
- Correct Answer
- 2:1
ExplanationWe are asked to find the ratio in which two varieties of sugar, costing Rs. 18 per kg and Rs. 24 per kg, should be mixed to get a mixture that costs Rs. 20 per kg. Here's the step-by-step approach:
- Let the quantities of the two varieties of sugar be:
- Let the quantity of sugar at Rs. 18 per kg be
xkg. - Let the quantity of sugar at Rs. 24 per kg be
ykg.
- Let the quantity of sugar at Rs. 18 per kg be
- Cost equation for the mixture:
- The total cost of the sugar mixture is the sum of the costs of the two varieties of sugar.
- The cost of the sugar at Rs. 18 per kg is
18xand the cost of the sugar at Rs. 24 per kg is24y. - The total weight of the mixture is
x + ykg, and we want the cost of the mixture to be Rs. 20 per kg. - The total cost of the mixture should be
20(x + y)rupees.
Thus, the cost equation becomes:
18x + 24y = 20(x + y) - Simplify the equation:
- Expanding the equation:
18x + 24y = 20x + 20y - Now, bring like terms together:
18x - 20x = 20y - 24y - This simplifies to:
-2x = -4y - Dividing both sides by -2:
x = 2y
- Expanding the equation:
- Conclusion:
- The ratio of
xtoyisx/y = 2/1. - Therefore, the two varieties of sugar should be mixed in the ratio of 2:1.
- The ratio of
- Final answer:
The two varieties of sugar should be mixed in the ratio 2:1.
- Let the quantities of the two varieties of sugar be:
- 1. Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is?
Options- A. 193 : 122
- B. 97 : 102
- C. 115 : 201
- D. 147 : 185 Discuss
- 2. One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.
Options- A. 27 %
- B. 26 %
- C. 29 %
- D. 21 % Discuss
- 3. The concentration of glucose in three different mixtures (glucose and alcohol) is 12,35 and 45 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. What is the ratio of glucose and alcohol in the new mixture?
Options- A. 3:2
- B. 4:3
- C. 2:3
- D. 3:4 Discuss
- 4. Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C.
Options- A. 1:9
- B. 9:1
- C. 3:7
- D. 7:3 Discuss
- 5. A mixture of 70 litres of Fruit Juice and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12.5% water?
Options- A. 2 lit
- B. 4 lit
- C. 1 lit
- D. 3 lit Discuss
- 6. The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
Options- A. 8:3
- B. 6:7
- C. 7:5
- D. 11:7 Discuss
- 7. An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?
Options- A. 45 gm
- B. 50 gm
- C. 55 gm
- D. 60 gm Discuss
- 8. A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, the profit %?
Options- A. 22.5%
- B. 25%
- C. 20%
- D. 33.33% Discuss
- 9. There are two mixtures of honey and water in which the ratio of honey and water are as 1:3 and 3:1 respectively. Two litres are drawn from first mixture and 3 litres from second mixture, are mixed to form another mixture. What is the ratio of honey and water in it?
Options- A. 111:108
- B. 11:9
- C. 103:72
- D. None Discuss
- 10. In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?
Options- A. 1:2
- B. 3:2
- C. 2:1
- D. 2:3 Discuss
Alligation or Mixture problems
Search Results
Correct Answer: 193 : 122
Explanation:
Given the three mixtures ratio as (1:2),(2:3),(3:4)
(1+2),(2+3),(3+4)
Total content = 3,5,7
Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105
105/3 = 35 , 105/5 = 21 , 105/7 = 15
Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)
i.e (35,70), (42,63), (45,60)
So overall mixture ratio of milk and water is
35+42+45 : 70+63+60
122:193
But in the question asked the ratio of water to milk = 193 : 122
Correct Answer: 27 %
Explanation:
Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135
X = 27
So, required percentage of benzene = 27 %
Correct Answer: 3:2
Explanation:
Concentration of glucose are in the ratio =
Quantity of glucose taken from A = 1 liter out of 2
Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit
Quantity of glucose taken from C = 0.8 lit
So, total quantity of glucose taken from A,B and C = 3.6 lit
So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit
Ratio of glucose to alcohol = 3.6/2.4 = 3:2
Correct Answer: 7:3
Explanation:
Ratio of Milk and water in a vessel A is 4 : 1
Ratio of Milk and water in a vessel B is 3 : 2
Ratio of only milk in vessel A = 4 : 5
Ratio of only milk in vessel B = 3 : 5
Let 'x' be the quantity of milk in vessel C
Now as equal quantities are taken out from both vessels A & B
=> 4/5 : 3/5
x
3/5-x x - 4/5
=> = (equal quantities)
=> x = 7/10
Therefore, quantity of milk in vessel C = 7
=> Water quantity = 10 - 7 = 3
Hence the ratio of milk & water in vessel 3 is 7 : 3
Correct Answer: 2 lit
Explanation:
Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres.
After adding water, juice would form 87.5% of the mixture.
Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
Correct Answer: 7:5
Explanation:
Milk in 1-litre mixture of A = 4/7 litre.
Milk in 1-litre mixture of B = 2/5 litre.
Milk in 1-litre mixture of C = 1/2 litre.
By rule of alligation we have required ratio X:Y
X : Y
4/7 2/5
\ /
(Mean ratio)
(1/2)
/ \
(1/2 ? 2/5) : (4/7 ? 1/2)
1/10 1/1 4
So Required ratio = X : Y = 1/10 : 1/14 = 7:5
Correct Answer: 50 gm
Explanation:
Initial quantity of copper = = 40 g
And that of Bronze = 50 - 40 = 10 g
Let 'p' gm of copper is added to the mixture
=> = 40 + p
=> 45 + 0.9p = 40 + p
=> p = 50 g
Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.
Correct Answer: 25%
Explanation:
As water costs free, water sold at cost price of milk gives the profit.
Required profit % = 5/20 x 100 = 5 x 5 = 25%.
Correct Answer: 11:9
Explanation:
From the given data,
The part of honey in the first mixture = 1/4
The part of honey in the second mixture = 3/4
Let the part of honey in the third mixture = x
Then,
1/4 3/4
x
(3/4)-x x-(1/4)
Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3
=>
=> Solving we get the part of honey in the third mixture as 11/20
=> the remaining part of the mixture is water = 9/20
Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .
Correct Answer: 2:1
Explanation:
Given rate of wheat at cheap = Rs. 2.90/kg
Rate of wheat at cost = Rs. 3.20/kg
Mixture rate = Rs. 3/kg
Ratio of mixture =
2.90 3.20
3
(3.20 - 3 = 0.20) (3 - 2.90 = 0.10)
0.20 : 0.10 = 2:1
Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.
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