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36.	The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?
	A.  4
	B.  8
	C.  12
	D.  16

Solution

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let the ten's and unit's digits be 2x and x respectively. Then, (10 + 2x + x) - (10x + 2x)= 36. ‹=›9x = 36 ‹=› x = 4. Required difference = (2x + x) - (2x - x) ‹=›2x = 8.

37.	The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is
	A.  23
	B.  40
	C.  80
	D.  120

Solution

Let the numbers be x and y. Then, xy = 120 and x2 + y2 = 289. ‹=›(x + y)2 = x2 + y2 + 2xy ‹=›289 + 240 ‹=›529 Therefore x + y = √529 = 23.

38.	A number of two digits has 3 for its unit's digit, and the sum of digits is 1/7 of the number itself. The number is
	A.  43
	B.  53
	C.  63
	D.  73

Solution

Let the ten's digit be x. Then, number = 10x + 3 and the sum of digits = (x + 3). So, (x + 3) = 1 / 7 (10 x + 3) ‹=› 7x + 21 = 10x + 3 ‹=›3x = 18. ‹=›x = 6. Hence, the number is 63.

39.	The sum of two numbers is 25 and their difference is 13. Find their product.
	A.  9
	B.  12
	C.  15
	D.  18

Solution

Let the numbers be x and y. Then, x + y = 33 ------(I) x - y = 15 -----(II) ‹=›Solving (I) and (II), we get x = 24, y= 9. ‹=›Smaller number = 9.