Question

Divide 45 into four parts such that when 2 is added to the first part 2 is subtracted from the second part 2 is multiplied
by the third part and the fourth partis divided by two, all result in the same number
16.24,10140
4,62510
312 5.20
8,12,18 20
​

Answer 1

Answer:

8, 12, 20, 5

None of the above options

Solution:

$Let \: \: us \: \: assume, \\ 4 \: \: parts \: \: are : P, \: \: Q, \: \: R \: \: and \: \: S \\ And \: \: common \: \: result \: \: is \: \: x \\ Then, \\ P = x + 2 \\ Q = x - 2 \\ R = x × 2 \\ S = \frac{x}{2} \\ \\ Then, \\ The \: \: numbers \: \: are : x + 2, \: \: x - 2, \: \: 2x, \: \: \frac{x}{2} \\ And \\ (x + 2) + (x - 2) + (2x) + ( \frac{x}{2} ) = 45 \\ \\ (x + 2) + (x - 2) + (2x) + ( \frac{x}{2} ) = 45 \\ x \cancel{ + 2} + x \cancel{ - 2 }+ 2x + \frac{x}{2} = 45 \\ x + x + 2x + \frac{x}{2} = 45 \\ \frac{2x + 2x + 4x + x}{2} = 45 \\ \frac{9x}{2} = 45 \\ 9x = 45 \times 2 \\ 9x = 90 \\ x = \frac{ \cancel{ 90} _{ \: \: 10} }{ \cancel 9_{ \: \: 1} } \\ x = \underline{ \underline{ 10}} \\ \\ Then, \: \: the \: \: 4 \: \: parts \: \: are : \\ P = x + 2 = 10 + 2 = 12 \\ Q = x - 2 = 10 - 2 = 8 \\ R = x × 2 = 10 \times 2 = 20 \\ S = \frac{x}{2} = \frac{10}{2} =5 \\ \\ Hence, \: \: the \: \: numbers \: \: are :12, \: \: 8, \: \: 20 , \: \: 5\\ 12 + 8 + 20 + 5 = 45$