Question

Of the three distinct numbers, if the sum of the first two is 25, the sum of second and twice the third is 45 and the sum of third and twice the first is 40, then the third number is

• A. 13
• B. 14
• C. 16
• D. 12

Answer 1

The correct option is C 16

Let the three distinct numbers be x, y and z.

$\text{Given:}x+y=25,\dots ..\left(i\right)$

$y+2z=45,\dots ..\left(ii\right)$

$z+2x=40\dots ..\left(iii\right)$

$\text{From}\left(i\right),y=25–x$

$\text{Substituting}y=25–xin\left(ii\right),\text{we get}$

$25–x+2z=45$

$\Rightarrow –x+2z=20\dots ..\left(iv\right)$

$\text{Multiplying (iv) by 2, we get}$

$–2x+4z=40\dots ..\left(v\right)$

$\text{Now, adding (iii) and (v), we get}$

$(–2x+4z)+(z+2x)=40+40$

$\Rightarrow 5z=80$

$\Rightarrow z=16$

Thus, the third number is 16.
Hence, the correct answer is option (3).