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Equations
A number is double and than increased by nine. the result is ninety-one. what is the original number?
Solution
If the two consecutive numbers one-fourth of the smaller one exceeds the one-fifth of the larger one by 3. find the numbers.
Solution
A father is 28 years older than the son. In 5 years the father's age will be 7 years more than twice that of the son. Find their present ages.
Solution
A person receives a total return of Rs. 402 from an investment of Rs. 8001 in two debenture issues of a company. The first one carrying an interest of 6% p.a. was bought for Rs. 100 each and the other one carrying an interest rate of 5% p.a. were bought at Rs. 105 each. Find the sum invested in each type of debentures.
Solution
The speed of a boat in still water is 10 km per hour. If it can travel 24 km downstream and 14 km in the upstream in equal time, indicate the speed of the flow of stream.
Solution
Mr. Roy buys 100 units of the Unit Trust of India at Rs. 10.30 per unit. He purchases another lot of 200 at Rs. 10.40 per unit. At Rs. 10.50 per unit, he takes up another lot of 400 and a further lot of 300 at Rs. 10.80 per unit. He watches as the price goes down and desires to take up as many units at Rs. 10.25 per unit as would make the average cost of his holding to Rs. 10.50 per unit. Assuming that Mr. Roy always buys units in multiples of 100., find the number of units he purchases at the lowest price of Rs. 10.25 per unit.
Solution
Demand for goods of an industry is given by the equation pq=100, where p is the price and q is quantity, supply is given by the equation 20 + 3p=q. What is the equilibrium price and quantity?
Solution
By selling a table for Rs. 56, gain is as much percent as its costs in rupees. What is the cost price?
Solution
A horse and a cow were sold for Rs. 3040 making a profit of 25% on the horse and 10% on the cow. By selling them for Rs. 3070 the profit realized would have been 10% on horse and 25% on the cow. Find the cost price of each.
Solution
In a perfect competition, the demand curve of a commodity is D=20-3p-p² and the supply curve is S=5p-1, where p is price, D is demand and S is supply. Find the equilibrium price and the quantity exchanged.
Solution
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