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### Question

If 7% of A + B = 11% of A - B, then what percent of B is A?

**A**

$4{1/2}$ %.

**B**

$5{1/2}$ %.

**C**

$3{1/2}$ %.

**D**

$3{3/4}$ %.

**Soln.**

**Ans: a**

We have been given 7% of A + B = 11% of A - B, so ${A + B}/{A - B}$ = $11/7$. By componendo and dividendo, ${(A + B) + (A - B)}/{(A + B) - (A - B)}$ = ${11 + 7}/{11 - 7}$, which gives $A/B$ = $18/4$ = ${9/2}$, which is same as: $4{1/2}$%