Question

. The production of refrigerators in a factory rose from
40000 to 48400 in 2 years. Find the rate of growth
p.a.​

Answer 1

Answer:

Let the rate of growth per annum be R.

We have, Present production =48400 scooters.

Previous production =40000 scooters

Number of years =2

∴48400=40000×(1+

100

R

)

2

⇒

40000

48400

=(1+

100

R

)

2

⇒

400

484

=(1+

100

R

)

2

⇒

100

121

=(1+

100

R

)

2

⇒(1+

100

R

)

2

=(

10

11

)

2

⇒1+

100

R

=

10

11

⇒

100

R

=

10

11

−1

⇒

100

R

=

10

1

⇒R=

10

100

=10

Hence, the required rate of growth =10% per annum.

Answer 2

Answer:

$484000 = 40000(1 + \frac{r}{100})^{2} \\ \frac{48400}{4000} = (1 + \frac{r}{100}) {}^{2} \\ \frac{121}{100} = (1 + \frac{r}{100} ){}^{2} \\ (\frac{11}{10} ) {}^{2} = (1 + \frac{r}{100} ) {}^{2} \\ \frac{11}{10} - 1 = \frac{r}{100} \\ \frac{1}{10} = \frac{r}{100} \\ r = \frac{100}{10} \\ r = 10 \% \: p.a.$