Problems on Numbers

Question:
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

[A].

20

[B].

23

[C].

169

[D].

None of these

Answer: Option B

Explanation:

Let the numbers be x and y.

Then, xy = 120 and x2 + y2 = 289.

(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529

x + y = 529 = 23.

Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

[A].

380

[B].

395

[C].

400

[D].

425

Answer: Option C

Explanation:

Let the numbers be x and y.

Then, xy = 9375 and	x	= 15.
	y

xy	=	9375
(x/y)		15

y2 = 625.

y = 25.

x = 15y = (15 x 25) = 375.

Sum of the numbers = x + y = 375 + 25 = 400.

Question:
The sum of two number is 25 and their difference is 13. Find their product.

[A].

104

[B].

114

[C].

315

[D].

325

Answer: Option B

Explanation:

Let the numbers be x and y.

Then, x + y = 25 and x – y = 13.

4xy = (x + y)2 – (x- y)2

   = (25)2 – (13)2

   = (625 – 169)

   = 456

xy = 114.

Question:
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

[A].

3

[B].

10

[C].

17

[D].

20

Answer: Option A

Explanation:

Let the number be x.

Then, x + 17 =	60
	x

x2 + 17x – 60 = 0

(x + 20)(x – 3) = 0

x = 3.

Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is:
[A].

35

[B].

36

[C].

45

[D].

54

Answer: Option D

Explanation:

Let the number be x.

Then,	1	of	1	of x = 15      x = 15 x 3 x 4 = 180.
	3		4

So, required number =		3	x 180		= 54.
		10

Video Explanation: https://youtu.be/z49OUnzTnwY