Answer

Verified

378.9k+ views

**Hint:**We will use the formula which states that:-

Present Production = Initial Production \[ \times {\left( {1 + \dfrac{R}{{100}}} \right)^n}\], where R = Rate of Increase, n = number of years

We will put in the given values and thus eventual finding R.

**Complete step-by-step answer:**

We have Initial Production = 40000 and Production after two years = 48400

So, now we will use the formula:- Present Production = Initial Production \[ \times {\left( {1 + \dfrac{R}{{100}}} \right)^n}\],

where R = Rate of Increase and n = number of years.

$\therefore $ we have 48400 = 40000 \[ \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}\]

Now, we will bring 40000 from R.H.S. to L.H.S.

$\therefore \dfrac{{48400}}{{40000}} = {\left( {1 + \dfrac{R}{{100}}} \right)^2}$

We will take square roots on both sides.

$\therefore \sqrt {\dfrac{{48400}}{{40000}}} = 1 + \dfrac{R}{{100}}$ ……(1)

We will rewrite 48400 and 40000 as squares of some numbers like:-

48400 = $220 \times 220 = {220^2}$

40000 = $200 \times 200 = {200^2}$

We will put these values in (1). We will get:-

$\therefore \sqrt {{{\left( {\dfrac{{220}}{{200}}} \right)}^2}} = 1 + \dfrac{R}{{100}}$

We know that the square root will cut off the square. So, we have:-

$\therefore \dfrac{{220}}{{200}} = 1 + \dfrac{R}{{100}}$

We can rewrite it as:-

$\dfrac{R}{{100}} + 1 = \dfrac{{220}}{{200}}$

We will now subtract 1 from both sides.

So, we get:- $\dfrac{R}{{100}} + 1 - 1 = \dfrac{{220}}{{200}} - 1$

Simplifying it by taking L.C.M. on R.H.S.

$\dfrac{R}{{100}} = \dfrac{{220 - 200}}{{200}}$

Now simplifying it more, we have:-

$\dfrac{R}{{100}} = \dfrac{{20}}{{200}}$

Now, we will take the 100 from the denominator of L.H.S. to R.H.S.

$\therefore R = \dfrac{{20 \times 100}}{{200}} = \dfrac{{2000}}{{200}} = 10$

Hence, the rate is 10%.

**So, the correct answer is “Option B”.**

**Note:**We need to learn the formula Present Production = Initial Production \[ \times {\left( {1 + \dfrac{R}{{100}}} \right)^n}\],

where R = Rate of Increase and n = number of years.

We need to remember the units of n in general formulas are years but we may be sometimes provided with data in months or weeks, then we will have to convert that data in years to use the formula correctly. Always remember to take the ${n^{th}}$root because we have n in the formula. Here, we have taken n to be 2. So, it is a possibility that we may learn the formula with 2 instead of n.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a stanza wise summary of money madness class 11 english CBSE

Which places in India experience sunrise first and class 9 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Which neighbouring country does not share a boundary class 9 social science CBSE

What is Whales collective noun class 10 english CBSE