Question

Latika delivers bottled water to stores in Delhi. She delivers to MTG's bookstore every 6th day and to Sammy's Bookstore every 9th day. On Thursday the 4th, she will deliver water to both of these stores. How many days after that will she deliver to both stores on the same day again?

• A. $17$
• B. $18$
• C. $19$
• D. $16$

Answer 1

Answer: (B)

$18$

After $4$th, Latika delivers to MTG on $10,16,....$

$\Rightarrow$ A.P. with $a=10$, $d=6$ & to Sameer's on $13,27,....$

$\Rightarrow$ A.P with $a=13,d=9$

As $a_n=a+(n-1)d$, for same term on both A.P., $10+(n_1-1)6=13+(n_2-1)9$

$\Rightarrow 3+9n_2-6n_1-3=0$

$\Rightarrow 3(3n_2-2n_1)=0$

$\Rightarrow 3n_2=2n_1$

$\Rightarrow n_2=\frac{2}{3}\left(n_1\right)$

But $n_2\in N$

$\Rightarrow n_1=3$, $n_2=2$ is $3$ first possibility

$\Rightarrow 10+\left(2\right)\left(6\right)={22}^{th}$

$\Rightarrow$ After $(22-4)=18$ days