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Q.1   The students of a school stand in a rectangle for an assembly. Each row had 8 boys and each column had 10 girls. There were 16 empty spaces in the rectangle. What is the number of possible values for the total number of students in the school?

Q 2 A school allows either all white uniform or a combination uniform where one of the trouser or shirt is black and the other is white. In all there are 15 combination uniforms, 12 white trousers and 13 white shirts. What is the total number of students in the school?

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Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.


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Find the number of real values of ‘k’ which satisfy the equation 5{k} + 4k = 6[k] + 3, where [k] is the greatest integer less than or equal to k and {k} is the fractional part of k.

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