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An express train leaves a station A at 6.45 p.m and reaches a station B 150 km away at 10.30 p.m. Time taken by the train to reach the next station C at a distance of 160 km away from station B with the same speed is

An express train leaves a station A at 6.45 p.m and reaches a station B 150 km away at 10.30 p.m. Time taken by the train to reach the next station C at a distance of 160 km away from station B with the same speed is
a. 4 hours - ans
b. 3 hours
c. 3 3/4 hours
d. 4 1/2 hours
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Find the number of perfect squares in the given series 2013, 2020, 2027,.

Find the number of perfect squares in the given series 2013, 2020, 2027,................, 2300   (Hint 44^2=1936) a. 1   b. 2    c. 3   d. Can’t be determined Answer: a Explanation: The given series is an AP with common difference of 7. So the terms in the above series are in the form of 2013 + 7k.  We have to find the perfect squares in this format in the given series. Given that 44^2 = 1936. Shortcut: To find the next perfect square, add 45th odd number to 44^2. So 45^2 = 1936 + (2 x 45 -1) = 2025 46^2 = 2025 + (2 x 46 - 1) = 2116 47^2 = 2116 + (2 x 47 - 1) = 2209 Now subtract 2013 from the above numbers and divide by 7. Only 2209 is in the format of 2013 + 7k.  One number satisfies.
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