Question

$a,b,c,d,e$ are five integers such that $a+b=b+c=c+d=d+e=2015$, $a+b+c+d+e=5030$, then $(d-a)$ is

• A. $12$
• B. $15$
• C. $18$
• D. $0$

Answer 1

The correct option is B $15$

Consider the equation,

$a+b=b+c=c+d=d+e=2015$(Given)

$a+b+c+d+e=5030$ (Given)

Now,

$(a+b)+(b+c)+(c+d)+(d+e)=2015+2015+2015+2015$

$a+2b+2c+2d+e=8060$

$a+b+c+d+e=5030$ substitute in the above expression,

$b+c+d=3030$

$d=1015$

$a+2(b+c)+d+d+e=8060$

$a+4030+1015+2015=8060$

$a=8060-7060$

$a=1000$

$d-a=1015-1000$

$d-a=15$

Hence, $d-a=15$