Number System
Sum of square of first number and cube of second number together is 568. Also square of the second number is 15 less than square of 8. What is the value of three-fifth of the first number ?
Let the first number be x and the second number be y.∴ y² = 82 - 15 = 64 - 15 = 49∴ y = 7∴ x² + 73 = 568= x² + 343 = 568= x² + 568 - 343 = 225∴ x = √225 = 15∴ 15 x 3/5 = 9
Average of 8 consecutive odd numbers = 656/8 = 82∴ Fourth number = 82 - 1 = 81∴ First numbers = 75Average of 4 even numbers = 87∴ Second even number = 87 - 1 = 86Second largest even number = 88∴ Required sum = 75 + 88 = 163
Let the number be 10x + y.∴ x + y = 12 ...........(i)10x + y - (10x + x) = 18or 10x + y - 10y - x = 18or 9x - 9y = 18∴ x - y = 2From (i) and (ii), x = 7, y = 5∴ Number = 75
Let the number of children be 'x' Therefore, each child will receiveX x 60/100 = 3x/5 chocolates∴ X x 3x/5 = 735∴ x² x 735x5/3 = 1225∴ x = 1225 = 35∴ Number of chocolates = 3x/5 = 21
EXAMIANS