Question

John planted $3$ plants in his garden area in $15$ minutes. He planted $6$ plants in $30$ minutes and $9$ plants in $45$ minutes. How much time John will take to plant $24$ plants $?$

• A. $110$ minutes
• B. $115$ minutes
• C. $120$ minutes
• D. $130$ minutes

Answer 1

The correct option is C $120$ minutes

Given data:


Let's first observe the sequence for the number of plants, planted by John.
$3$, $6$, $9$, . . .

$\bullet$ Difference between $2$nd term and $1$st term $=6-3=3$
$\bullet$ Difference between $3$rd term and $2$nd term $=9-6=3$

$\therefore$ There is a difference of $3$ in two consecutive terms, i.e., if we add $3$ with the previous term, we will get the next term. So, the sequence would be:
$3$, $6$, $9$, $12$, $15$, $18$, $21$, $\underset{–}{24}$

$\text{Need to find:}$ How much time John will take to plant $24$ plants?

Let's observe now the sequence of time (in minutes) taken by John to plant different number of plants.
$15$, $30$, $45$, . . .

$\bullet$ Difference between $2$nd term and $1$st term $=30-15=15$
$\bullet$ Difference between $3$rd term and $2$nd term $=45-30=15$

$\therefore$ There is a difference of $15$ minutes in two consecutive terms, i.e., if we add $15$ minutes with the previous term, we will get the amount of time John will take to plant next number of plants. So, the sequence would be:
$15$, $30$, $45$, $60$, $75$, $90$, $105$, $120$

After summarizing the number of plants and the respective time taken to plant by John, we get

Number of plants	Time taken to plant (in minutes)
$3$	$15$
$6$	$30$
$9$	$45$
$12$	$60$
$15$	$75$
$18$	$90$
$21$	$105$
$\underset{–}{24}$	$\underset{–}{120}$

Hence, John will take $\underset{–}{120\text{minutes}}$ to plant $\underset{–}{24\text{plants}}$, i.e., option (c.) is the correct one.