Question

if neeta can knit a sweater in 8 days and kirti can knit a similar sweater in 12 days if both of them and radha knit in 16 days in how many days will radha alone knit a sweater

Answer 1

4 days
if neeta takes 8days (X) and similarly for kriti in 12 days (Y).
X+Y+Z=16 days
8+12+Z=16
Z=4 days (therefore radha alone takes 4 days to knit a sweater)

Answer 2

Radha alone knit a sweater in 6 days.

Step-by-step explanation:

Let us assume that Radha knit the sweater in x days.

Now, Neeta knit it in 8 days and Kriti knit it in 12 days.

Therefore, they together will knit in one day ($\frac{1}{8} + \frac{1}{12} + \frac{1}{x}$) part of the sweater.

=  $\frac{3x + 2x + 24}{24x}$ part of the sweater.

So, they will knit the sweater in $\frac{24x}{3x + 2x + 24}$ days.

Given that, $6(\frac{24x}{3x + 2x + 24}) = 16$

⇒ 144x = 48x + 32x + 384

⇒ 64x = 384

⇒ x = 6 days.

So, Radha alone knit a sweater in 6 days. (Answer)