Question

If 72 is divided into two parts such that sum of 5 times the first part and 11 times the second part is 492, then the difference between two parts is

• A. 37
• B. 50
• C. 28
• D. 22

Answer 1

The correct option is C 28

Let the two parts. be x and y.
According to the question,
x + y = 72 . . . (i)
5x + 11y = 492 . . . (ii)
Multiplying (i) by 5, we get
5x + 5y = 360 . . .(iii)
Substracting (iii) from (ii), we get
(5x + 11y) - (5x + 5y) = 492 - 360
$\Rightarrow$ 5x + 11y - 5x - 5y = 132
$\Rightarrow$ 6y = 132
$\Rightarrow$ y = 22
Now, substituting the value of y in (i), we get
x + 22 = 72
⇒ x = 50
Thus, the difference between the two parts is 50 – 22 = 28
Hence, the correct answer is option (3).