Arithmetic Sufficiency

Q: What is the ratio in which two varieties of sugar at Rs. 20/kg and Rs. 30/kg must be mixed? I. The mixture is sold at Rs. 28/kg. II. There is a 12% profit on selling the mixture.

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). Selling price alone (I) doesn't give cost price. Together, CP of mixture = 28 / 1.12 = Rs. 25. Using alligation: (30-25) : (25-20) = 5:5 = 1:1. Both are required.

Q: A container has 40 liters of milk mixture. How much water must be added to it? I. The original concentration of milk is 100%. II. The final concentration of milk becomes 80%.

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). Together: Initially, 40L pure milk. Let W liters of water be added. 40 / (40 + W) = 0.8 => 32 + 0.8W = 40 => 0.8W = 8 => W = 10 liters. Both are required.

Q: What is the percentage of copper in the final alloy? I. Alloy A has 20% copper and Alloy B has 40% copper. II. Alloy A and Alloy B are mixed in a 3:2 ratio by weight.

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). Together, weighted average percentage = (3*20 + 2*40) / 5 = 140 / 5 = 28%. Both statements are required.

Q: What is the total capacity of the wine barrel? I. 10 liters of wine is replaced with water, and this process is done twice in total. II. The final ratio of wine to water in the b...

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). From II, Final Wine / Total = 16/25. From I, formula: Final/Total = (1 - Draw/Capacity)^n. Together: (1 - 10/C)^2 = 16/25 => 1 - 10/C = 4/5 => C = 50 liters. Both are required.

Q: How many liters of pure water is in the mixture? I. The mixture contains milk and water in a 4:1 ratio. II. The price of the mixture is Rs. 32 per liter.

Correct Answer: Option D (Statements I and II together are not sufficient.). We have the ratio, but we lack the total volume of the mixture AND the individual prices of milk/water to use alligation. The data is entirely insufficient even with both statements.

50 Questions

Practice Arithmetic Sufficiency questions with answers and step-by-step solutions. These problems are curated from recent campus placement test papers (TCS, Infosys, Wipro, Cognizant, Accenture) and competitive government exams (SSC CGL, Bank PO, RRB NTPC, UPSC).

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Arithmetic Sufficiency: Directions & Problem Statements Shared for questions below

DirectionsSet 6: Mixtures & Alligations

Q26

What is the ratio in which two varieties of sugar at Rs. 20/kg and Rs. 30/kg must be mixed?
I. The mixture is sold at Rs. 28/kg.
II. There is a 12% profit on selling the mixture.

medium

Q27

A container has 40 liters of milk mixture. How much water must be added to it?
I. The original concentration of milk is 100%.
II. The final concentration of milk becomes 80%.

medium

Q28

What is the percentage of copper in the final alloy?
I. Alloy A has 20% copper and Alloy B has 40% copper.
II. Alloy A and Alloy B are mixed in a 3:2 ratio by weight.

medium

Q29

What is the total capacity of the wine barrel?
I. 10 liters of wine is replaced with water, and this process is done twice in total.
II. The final ratio of wine to water in the barrel is 16:9.

medium

Q30

How many liters of pure water is in the mixture?
I. The mixture contains milk and water in a 4:1 ratio.
II. The price of the mixture is Rs. 32 per liter.

medium

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Arithmetic Sufficiency

What is the ratio in which two varieties of sugar at Rs. 20/kg and Rs. 30/kg must be mixed?
I. The mixture is sold at Rs. 28/kg.
II. There is a 12% profit on selling the mixture.

Community Discussion & Shortcut Formulas

A container has 40 liters of milk mixture. How much water must be added to it?
I. The original concentration of milk is 100%.
II. The final concentration of milk becomes 80%.

Community Discussion & Shortcut Formulas

What is the percentage of copper in the final alloy?
I. Alloy A has 20% copper and Alloy B has 40% copper.
II. Alloy A and Alloy B are mixed in a 3:2 ratio by weight.

Community Discussion & Shortcut Formulas

What is the total capacity of the wine barrel?
I. 10 liters of wine is replaced with water, and this process is done twice in total.
II. The final ratio of wine to water in the barrel is 16:9.

Community Discussion & Shortcut Formulas

How many liters of pure water is in the mixture?
I. The mixture contains milk and water in a 4:1 ratio.
II. The price of the mixture is Rs. 32 per liter.

Community Discussion & Shortcut Formulas

Arithmetic Sufficiency

What is the ratio in which two varieties of sugar at Rs. 20/kg and Rs. 30/kg must be mixed? I. The mixture is sold at Rs. 28/kg. II. There is a 12% profit on selling the mixture.

Community Discussion & Shortcut Formulas

A container has 40 liters of milk mixture. How much water must be added to it? I. The original concentration of milk is 100%. II. The final concentration of milk becomes 80%.

Community Discussion & Shortcut Formulas

What is the percentage of copper in the final alloy? I. Alloy A has 20% copper and Alloy B has 40% copper. II. Alloy A and Alloy B are mixed in a 3:2 ratio by weight.

Community Discussion & Shortcut Formulas

What is the total capacity of the wine barrel? I. 10 liters of wine is replaced with water, and this process is done twice in total. II. The final ratio of wine to water in the barrel is 16:9.

Community Discussion & Shortcut Formulas

How many liters of pure water is in the mixture? I. The mixture contains milk and water in a 4:1 ratio. II. The price of the mixture is Rs. 32 per liter.

Community Discussion & Shortcut Formulas

What is the ratio in which two varieties of sugar at Rs. 20/kg and Rs. 30/kg must be mixed?
I. The mixture is sold at Rs. 28/kg.
II. There is a 12% profit on selling the mixture.

A container has 40 liters of milk mixture. How much water must be added to it?
I. The original concentration of milk is 100%.
II. The final concentration of milk becomes 80%.

What is the percentage of copper in the final alloy?
I. Alloy A has 20% copper and Alloy B has 40% copper.
II. Alloy A and Alloy B are mixed in a 3:2 ratio by weight.

What is the total capacity of the wine barrel?
I. 10 liters of wine is replaced with water, and this process is done twice in total.
II. The final ratio of wine to water in the barrel is 16:9.

How many liters of pure water is in the mixture?
I. The mixture contains milk and water in a 4:1 ratio.
II. The price of the mixture is Rs. 32 per liter.