Question

20 students can write 40 essays in 10 days. How many essays can 30 students write in 20 days?

• A. 100 essays
• B. 120 essays
• C. 80 essays
• D. 140 essays

Answer 1

The correct option is B 120 essays

Here, the number of essays are directly proportional to the number of boys and the number of days.

Given,

Number of essays	Number of students	Number of days
40	20	10
$x$	30	20
40 : $x$	20:30 = 2:3	10:20 = 1:2

Number of essays $\propto$ Number of students
$\Rightarrow 40:x=2:3...\left(i\right)$

Number of essays $\propto$ Number of days
$\Rightarrow 40:x=1:2...\left(ii\right)$
From (i) and (ii), we get,
40 : $x$
$=\text{compound ratio of}2:3\text{and}1:2$

$\Rightarrow 40:x=(2:3)\times (1:2)$
$\Rightarrow 40:x=(2\times 1):(3\times 2)$
$\Rightarrow 40:x=(2:6)or(1:3)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 1=40\times 3$
$\Rightarrow x=120$

So, 120 essays can be written by 30 students in 20 days.