Question

In winter, the temperature at a hill station from Monday to Friday is in A.P. The sum of the temperatures of Monday, Tuesday and Wednesday is zero and the sum of the temperatures of Thursday and Friday is $15$. Find the temperature of each of the five days.

• A. $-3,0,3,6,9$
• B. $-3,3,9,15,21$
• C. $-2,0,2,4,6$
• D. $0,3,6,9,12$

Answer 1

The correct option is A $-3,0,3,6,9$

Let the temperature of the hill station from Monday to Friday which form are A.P. is

$a-2d,a-d,a,a+d,a+2d$

As per the first condition

$a-2d+a-d+a=0$

$\therefore 3a-3d=0$

$\Rightarrow 3(a-d)=0$

$\Rightarrow (a-d)=0$

$\therefore a=d$

As per the second condition

$a+d+a+2d=15$

$\therefore 2a+3d=15$

$\Rightarrow 2a+3a=15(\because a=d)$

$\Rightarrow 5a=15$

$\Rightarrow a=3$

$\Rightarrow d=3$ $(a=d)$

$\therefore a-2d=3-2\left(3\right)=3-6=-3$

$\therefore a-d=3-3=0$

$\therefore a+d=3+3=6$

$\therefore a+2d=3+2\left(3\right)=9$

$\therefore$Temperature from Monday to Friday is $-3^{\circ }C,0^{\circ }C,3^{\circ }C,6^{\circ }C,9^{\circ }C$