PE 5 - Ratio | Arithmetic - Ratio, Proportion & Variation
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Volume of a sphere varies directly with cube of its radius. Three spheres with radii in the ratio 3 : 4 : 5 are melted to form a large sphere. What is the ratio of radius of smallest sphere to the new sphere formed.
- (a)
1 : 2
- (b)
1 : 3
- (c)
3 : 7
- (d)
None of these
Solution
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ReportA, B, C and D enter into partnership. A subscribes 1/3th of the capital, B, 1/4th and C ,1/5th and D the rest. What is the share of D out of a profit of Rs. 6,000?
- (a)
Rs. 2000
- (b)
Rs. 1600
- (c)
Rs. 1200
- (d)
Rs. 1300
Ankur has five times as much money with him as Varun does. Each day, Ankur spends a constant amount of money while Varun earns a fifth of the amount that Ankur spends. After 10 days, the ratio of the amounts with Ankur and Varun is 15 : 7. After-how many more days will the ratio of the amounts with them be 5 : 9?
- (a)
20
- (b)
15
- (c)
5
- (d)
10
A is a working partner and B is a sleeping partner in a business. A puts in Rs. 5000 and B puts in Rs. 6000. A receives 12 1/2% of the profit for managing, the rest being divided in proportion of their capital. What is the share of A out of a profit of Rs. 4400?
- (a)
Rs. 2100
- (b)
Rs. 2300
- (c)
Rs. 2200
- (d)
Rs. 2150
A, B, C and D entered into a partnership by investing the capital in the ratio of 2 : 3 : 5 : 4. If A invested the money for 9 months, B for 8 months, C for 4 months and D for 6 months. Find the share of C in the annual profit of Rs. 64500.
- (a)
Rs. 18000
- (b)
Rs. 15000
- (c)
Rs. 21000
- (d)
Rs. 16500
There are five identical cups containing milk in the ratio 4 : 5 : 6 : 7 : 8. How many cups are at least half full of milk if the total volume of milk in the cups is three-fifth of the total volume of the five cups?
The cost of a precious stone varies as the cube of its weight. A certain precious stone broke into three pieces whose weights are in the ratio 1 : 2 : 3, as a result of which its cost reduces by Rs. 36,000. What was the cost of the stone before breaking?
- (a)
Rs. 41600
- (b)
Rs. 43200
- (c)
Rs. 20480
- (d)
Rs. 21600
The total surface area of a cylinder having a certain height is the sum of 2 parts. One of the parts varies directly with its radius when height is constant & directly with its height when radius is constant. The other part varies directly with the square of its radius. The total surface areas of two cylinders having the same height whose radii are 5 cm and 10 cm are 1440 sq.cm and 5280 sq.cm respectively. Find the total surface area in sq.cm) of a cylinder of the same height whose radius is 15 cm.
A quantity Q equals the sum of three other quantities, the first of which is a constant, the second varies directly as x and the third varies directly as x². When x = 1; p = 52. when x = 2, p = 144 and when x = 3, p = 316. Find the constant.
The consumption of petrol per hour of my car varies directly as the square of its speed. When the car is travelling at 25 kmph its consumption is 4 litres. If each litre costs Rs. 15 and other expenses per hour are Rs. 100, then what should be the speed to minimize the expenditure to cover a distance of 200 km?
- (a)
25√5/√3
- (b)
25
- (c)
25√5
- (d)
None of these