How do i approximate growth related questions?I did not understand the procedure. :( Kindly help!

Hi,

There are a few ways in which you can approximate the numbers in growth related questions.

If you are solving a fraction, try to round off the numbers to the nearest multiple of 5. The simplification would be easier with this.

To approximately calculate the rate of growth, we can use the following method:

By Binomial Theorem,

$$(1+x)^n$$ = $$1$$ + $$nx$$ + $$^n C _2 x^2 $$ + $$^n C _3 x^3 $$ . . .

• If x is sufficiently small i.e. x<10% we can ignore higher powers of x in the binomial expansion

• If nx < 10%, the third term is less than 0.5%. If the options are sufficiently far apart we can approximate the expansion to 1+nx.

• If 10%< nx < 25% or the options are very close together, we can approximate the expansion to 1+nx+$$(n(n-1)/2) x^2$$

For e.g. if literacy grew from 20% to 35% in 5 years, what was the annual rate of growth?

Let r be the rate of growth. Hence, $$20% * (1+r)^5$$ = 35%. $$(1+r)^5$$ = 1.75. We can approximate the expansion to $$(1+r)^5$$ = 1 + 5r + $$10 r^2$$. Hence, $$10 r^2+5r-0.75$$=0. r = $$(-5+\sqrt{25+4*0.75*10})/20$$ = (7.4-5)/20 = 0.12 i.e. 12%. The actual value is 11.84% which is fairly close to what we got.

Remember that when r>-1 and n is non-negative integer, you are approximating up the value of r and approximating down the value of $$(1+r)^n$$. Hence, the approximate answer for r (12% in the example above) will be always greater than the actual value of r (11.84%).