Question

B as a percentage ofAis equal to Aas a
percentage of(A+B). How much percent
of A is B?
(a) 60%
(b) 62%
(C) 64%
(d) 66%

Answer 1

Answer:

Option (b), 62% is correct.

Step-by-step explanation:

By the given condition,

B/A = A/(A + B) ..... (1)

Now to find the percentage of A = B, we consider B = Ax. From (1), we get

Ax/A = A/(A + Ax)

or, x = 1/(1 + x)

or, x² + x - 1 = 0

Using quadratic formula, we get

x = {- 1 ± √(1 + 4)}/2

= (- 1 ± √5)/2

Since x cannot be negative, we take

x = (- 1 + √5)/2

≈ 0.62

Therefore the required percentage is

= 0.62 × 100%

= 62%

Answer 2

Answer:

Option => B.

62%

Step-by-step explanation:

Given -

B as a percentage of A is equal to A.

A percentage of (A + B).

To Find -

How much percent  of A is B.

Solution -

ATQ,

$\dfrac{B}{A}$ = $\dfrac{A}{(A + B)}$ .....Equation - (1)

Consider the -

The B as Ap.

So,

⇒ $\dfrac{Ap}{A}$ = $\dfrac{A}{(A + Ap)}$

⇒ p = $\dfrac{1}{(1 + p)}$

⇒ p² + p - 1 = 0.

According to quadratic formula,

$\sf\\ \\\implies p= \dfrac{{-1\± \sqrt{(1 + 4)}}}{2}\\ \\ \\ \implies \dfrac{(-1\± \sqrt 5)}{2}$

____________{ The value of p can't be negative! }

$\sf\\ \\\implies p= \dfrac{(- 1 + \sqrt5)}{2}\\ \\ \implies 0.62$

So,

$\sf \\ \\\implies 0.62 \times 100\% \\ \\ \implies 62\%$

∴ The correct option is B.