Questions and Answers
How many kilograms of provisions does the garrison consume daily for 2,000 men?
After 4 weeks, how many men are in the garrison?
What is the total amount of provisions initially available for the garrison?
What amount of provisions is consumed after 4 weeks by the garrison?
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With the new rate of 2 kg per day per man, how long will the remaining provisions last after 4 weeks?
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Calculate the area of a circle with a radius of 8 ft, given that the area of a circle with a radius of 7 ft is 196 sq ft.
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If A varies directly with B and inversely with C, what is the value of A when B is 9 and C is 6, given A is 16 at B = 28 and C = 7?
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What are the original numbers of men and women in a conference hall where the ratio changes from 5:4 to 7:6 after additional attendees join?
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What will be the value of b when a = 6, if a and b are inversely proportional and a = 8 gives b = 240?
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How many marks did Raju score in Maths if his marks in Maths, Physics, and Chemistry are in the ratio 2:3:4 and the total is 189?
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How many days will the food last for the remaining men after 25 leave, given provisions for 150 men for 45 days, and after 10 days?
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If x varies directly as the cube root of y, what is the value of x when y = 216 if x = 2 when y = 8?
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How long would 25 men take to complete five times a job if 18 men take 30 days working 10 hours a day?
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Study Notes
Area and Proportions
- The area of a circle grows with the square of its radius. Example: Area at radius 7 ft is 196 sq ft; at radius 8 ft, area is 256 sq ft.
Direct and Inverse Variation
- A varies directly with B (constant C) and inversely with C (constant B). Given A=16 when B=28 and C=7, A becomes 9 when B=9 and C=6.
Ratio of Men and Women
- Initial ratio of men to women in a conference is 5:4. Adding 3 men and 6 women changes the ratio to 7:6; initial counts are 60 men and 48 women.
Inverse Proportionality
- If quantities a and b are inversely proportional: when a=8, b=240. Thus, for a=6, b is found to be 320.
Ratio of Marks
- Raju's marks in Maths, Physics, and Chemistry are in the ratio 2:3:4, totaling 189 marks. Marks in Maths: 42.
Provisions and Time
- A fort had provisions for 150 men for 45 days. After 10 days and 25 men leaving, remaining provisions last for 42 more days for 125 men.
Direct Variation with Cube Root
- Variable x varies directly with the cube root of y. Given y=8 and x=2, if y=216, then x equals 18.
Work Completion Time
- Eighteen men complete work in 30 days at 10 hours/day. To finish five times that work, 25 men working 12 hours/day will take 90 days.
Contribution of Farmers
- Nine farmers plough 18 acres in 6 hours. Sixteen farmers can plough 112 acres in 21 hours.
Garrison Provisions
- A garrison of 2000 men has provisions for 20 weeks (2.5 kg/man/day). After 4 weeks and with 500 additional men, provisions last for another 16 weeks at 2 kg/man/day.
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Description
This quiz covers concepts from Arithmetic L9, specifically focusing on the relationship between area and radius in circles. Ideal for students in the GENESIS batch under Ronak Shah's guidance, it includes problem-solving questions to enhance understanding. Solutions are provided at the end for self-assessment.
