Question

Four wholes numbers added three at a time give sums $180,197,208$ and $222$ respectively. The largest of the four numbers is $.......$

• A. $87$
• B. $88$
• C. $89$
• D. $90$

Answer 1

Answer: (C)

$89$

Let the whole numbers are $a,b,candd$

Given $a+b+c=180..\left(1\right)$
$b+c+d=197..\left(2\right)$
$c+d+a=208..\left(3\right)$
$d+a+b=222..\left(4\right)$

$\left(4\right)-\left(1\right)=d-c=\mathrm{42..}\left(5\right)$
$\left(4\right)-\left(3\right)=b-c=14.\left(6\right)$
$\left(4\right)-\left(2\right)=a-c=25.\left(7\right)$
$\left(3\right)-\left(2\right)=a-b=11..\left(8\right)$

If $a=x,b=x-11$ (from eq8)
$c=x-25$ (from eqe 7)

$d=c+42$
$=x-25+42=x+17$

(from $eq5$ & $eq7$) $b+c+d=197$
$x-11+x-25+x+17=197$
$3x=197+19=216$
$\Rightarrow x=72$

$a=72,b=61,c=47,d=89$
Hence, option 'C' is correct.