Question

EXPLANATORY ANSWER NEEDED

If A's income is $26 \frac{2}{3} \%$ more than that of B, find how much per cent is B's income less than that of A.

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Answer 1

$\underline{\text{Answer :}}$

$\small{\text{B's income is 21.05\% less than that of A.}}$

$\underline{\text{Step by step solution :}}$

$\small{\text{Let, A's income to be A and for B, it is B.}}$

$\text{Given that,}$

$\text{Income of A}=26\frac{2}{3}\%\:\text{more than B}$

$\implies \mathrm{A = B + B \times 26\frac{2}{3}\%}$

$\implies \mathrm{A = B + B \times \frac{80}{3}\%}$

$\implies \mathrm{A = B + B \times \frac{80}{300}}$

$\implies \mathrm{A = (1 + \frac{80}{300}) B}$

$\implies \mathrm{A = \frac{380}{300} B}$

$\implies \mathrm{B = \frac{300}{380}A}$

$\implies \mathrm{B = (1 - \frac{80}{380}) A}$

$\implies \mathrm{B = A - \frac{80}{380} A}$

$\implies \mathrm{B = A - (\frac{80}{380} \times 100\%) A}$

$\implies \mathrm{B = A - 21.05\%A}$

$\boxed{\text{Income of B = 21.05\% less than A}}$

Answer 2

Answer:

21.05%

Step-by-step explanation:

Method - 1:

Let the income of B be 100.

Given that A's income is (80/3)% more than that of B.

Then, the income of A = (100 + 80/3% of 100)

                                     = (100 + 80/3% * 100)

                                     = 126.67

Difference = 126.67 - 100

                  = 26.67

%Difference = (26.67/126.67) * 100

                    = 21.05%

Therefore, B's income is 21.05% less than that of A.

Method - 2:

Required percentage = (100 * R/100 + R)%

= (100 * 80/3)/(100 + 80/3)

= (8000/3)/(380/3)

= 8000/380

= 400/19

= 21.05%.

Therefore, B's income is 21.05% less than that of A.

Hope it helps!