Question

If 3% of (a+b)=7% of (ab), and 5% of (a-b) = 4% of (ab) then what percent of b is a

Answer 1

204.35% of b is a.

Step-by-step explanation:

Given, 3% of (a + b) = 7% of (ab)

=> 3a + 3b = 7ab......................(i)

5% of (a - b) = 4% of (ab)

=> 5a - 5b = 4ab.....................(ii)

Now, 5 x equation(i) + 3 x equation(ii),

15a + 15b + 15a - 15b = 35ab + 12ab

=> 30a = 47ab

=> b = $\frac{30}{47}$

Plug the value of b in equation(i),

3a + 3 x $\frac{30}{47}$ = 7a$(\frac{30}{47})$

=> 3a + $\frac{90}{47}$ = $\frac{210a}{47}$

=> $\frac{210a}{47}$ - 3a = $\frac{90}{47}$

=> $\frac{69a}{47}$ = $\frac{90}{47}$

=> a = $\frac{90}{69}$ = $\frac{30}{23}$

Let x% of b = a

=> $\frac{x}{100}\times \frac{30}{47} = \frac{30}{23}$

=> x = $\frac{47}{23} \times 100$ = 204.35%

Hence, 204.35% of b is a.