Arithmetic – Variation

Q.1. The current flowing through a circuit is directly proportional to the voltage in the circuit? The current is measured as 4 amps when the voltage is 200 volts. What will be the voltage in the circuit when the current is 5.2 amps?
Q.2. At the rate of 28 lines per page, a book has 300 pages. If the book has to contain only 280 pages, how many lines should a page contain?
Q.3. a varies directly as \[ b^2 \], b = 11 when a = 7. What is the approximate value of a when b is 19?
Q.4. The intensity is light produced by a light source varies inversely as the square of the distance from the source. If the intensity of light produced at a distance of 3 feet from a light source is 750 lumnes, what is the intensity of light produced at 5 feet from the same source?
Q.5. Ram found a relation between the marks of Mahesh, Ramesh and Durgesh. The relation was such that the marks of Mahesh very jointly (and in direct proportion) with the square of the marks of Ramesh and the fourth power of the marks of Durgesh. By what percentage would the marks of Mahesh increase/decrease if the marks of Ramesh were doubled and those of Durgesh were halved?
Q.6. In Mumbai the electricity bill charging system is as follows. Every consumer pays a monthly service charge of Rs.750. Apart from that, Rs. 3 per unit is charged for the first 50 units, Rs. 2.5 per unit is charged for the next 80 units. Rs. 2 per unit for the next 100 units, Rs. 1.5 per unit for the next 150 units and Re. 1 per unit after that. If Prashant’s current monthly usage was 700 units, what will be his electric bill (in Rs.) for this month?
Q.7. It is known that current (I) in an electric circuit is inversely proportional to the resistance (R) in the circuit. When the resistance is 3 ohms, the current is 2 amperes. Find the resistance if the current is 5 amperes; and find the current when the resistance is 5 ohms.
Q.7. Dilwar’s group gives a hall on rent for wedding functions. There is a fixed cost for the hall and a cost per plate for the food provided. Anupan hired the hall for a plate count of 700 for 8 hours and paid Rs. 64,250 in all. Mr. Shukla hired the hall for 9 hours for a plate count of 550 and paid Rs. 52,500 in all. The bill for both individuals included a/c charges, which were Rs. 2,000 for 7 hours and Rs. 250 for every hour after that. If Mr. Negi wants to hire the same hall for 8 hours for 7550 plates, but without the A/c, what would be his total cost (in Rs.)?
Q.8. 6 typist working 5 hours a day can type the manuscript of a book in 16 days. How many days will 4 typists take to do the same job, each working 6 hours a day?
Q.9. 60 liters of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, how many liters of diesel is required to travel 800 km using 1200 cc engine?
Q.10. It takes 6 workers to lift 8 cars with 4 cranes. Also, the number of cranes (c) it takes for w workers to lift y cars varies directly as the number of cars and inversely as the number of workers. How many workers are required to lift 20 cars with 5 cranes?
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