1. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. Find his present age.
2. In a class test the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in
Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in two subjects.
3. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
4. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
5. A train travels 360 kms at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
6. Two water taps together can fill a tank in 9 3/8 hours. The tap of the larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank
7. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.
8. Sum of areas of two squares is 468 sqm. If the difference of their perimeters is 24 metres, find the sides of two squares.
9. Find two consecutive positive integers, sum of whose squares is 365.
10. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.
11. The altitude of a right angled triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
12. A train travels a distance of 480 kms at a uniform speed. If the speed had been 8 kmph less, then it would have taken 3 hrs more to cover the same distance. We need to find the speed of the train.
13. Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360. We need to find Rohan’s present age.
14. Solve by factorization a. 4x2 - 4a2x + (a4 – b4) = 0 b. (x – 3) (x – 4) = 34/332
15 A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original position. Find the depth of water in the pond.
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