self Maths Puzzle

How many two digit number exists ,which is x more than the square of an integer and 2x less than square of its consecutive integer ?

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self Other Question

Slide the red and yellow tiles to the Goal position shown above in less than 32 moves.
A invested Rs 80000 in a business. After few months B joined him with Rs 72000/ At the end of the year the total profit was divided between them in the ratio 4:3. The number of months after which B joined is