Same topic4 marksDifficulty: Hard
A train travels 300 km at a uniform speed. If the speed had been 5 km/h more, the journey would have taken 2 hours less. Find the original speed of the train.
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4 marksDifficulty: Hard
The sum of the squares of two consecutive natural numbers is 313. Find the numbers.
Original Khojo Papers practice question — not from a past board paper.
Answer
12 and 13
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
Let the numbers be n and n + 1. Then n2 + (n + 1)2 = 313, so 2n2 + 2n + 1 = 313 and n2 + n − 156 = 0. Factorising, (n + 13)(n − 12) = 0. As n is a natural number, n = 12 and the numbers are 12 and 13.
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