a2zinterviews

40.	Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3 : 4, the numbers are
	A.  6, 8
	B.  9, 12
	C.  12, 16
	D.  16, 20

Solution

Let the numbers be 3x and 4x. Then, (4x)2 = 8 x (3x)2 - 224 ‹=›16x2 = 72x2 - 224 ‹=›56x2 = 224. ‹=›x2 = 4. ‹=›x = 2. So, the numbers are 6 and 8.

41.	The sum of the digits of a two digit number is 15 and the difference between the digits is 3. What is the two digit number?
	A.  69
	B.  78
	C.  87
	D.  Cannot be determined

Solution

Let the ten's digit be x and unit's digits be y. Then, x + y = 15 and x - y = 3 or y - x = 3. Solving x + y = 15 and x - y = 3, we get : x = 9, y = 6. Solving x + y = 15 and y - x = 3, we get : x = 6, y = 9. So, the number is either 96 or 69. Hence the number cannot be determined.

42.	The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are
	A.  600, 400
	B.  628, 372
	C.  640, 360
	D.  None of these

Solution

Let the numbers be x and y. Then, x2 - y2 = 256000 and x + y = 1000. On dividing we get : x - y = 256. ‹=›Solving x + y = 1000 and x - y = 256, ‹=›we get : x = 628 and y = 372.