1.) Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?
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2.) A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
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3.) Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
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4.) A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
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5.) A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
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6.) If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
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7.) At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
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8.) In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see Fig.]. Find the length and breadth of the pond.
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9.) At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t2/4 minutes. Find t.
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Ans : 1.) 15 2.) 42 km/h 3.) 12 4.) 8 5.) 45 km/h 6.) 14 year 7.) 5 year, 27 year 8.) 34 m, 24 m 9.) 14