Question 51

Z is increased successively by $$11\frac{1}{9}$$% and 10% to get R. If R = 165, then what is the value of Z?

Solution

Z is increased successively by $$11\frac{1}{9}$$% and 10% to get R.

Z of $$(100+11\frac{1}{9})$$% of (100+10)% = R

Z of $$(100+\frac{100}{9})$$% of 110% = R

Z of $$\frac{1000}{9}$$% of 110% = R

Z of $$\frac{10}{9}$$ of 110% = R

If R = 165.

$$Z\times\frac{10}{9}\times\frac{110}{100}=165$$
$$Z\times\frac{1}{9}\times11=165$$

$$\frac{Z}{9}=15$$

Value of Z = 135

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