Question 71

A : B = 12 : 17 and A is 20% more than C. If B is 15% less than D, then C is what percentage of D?

Solution

A : B = 12 : 17.

Let's assume that A and B are 12y and 17y.

A is 20% more than C.

12y = C of (100+20)%

12y = C of 120%

$$12y=C\times\frac{120}{100}$$
$$y=C\times\frac{1}{10}$$
C = 10y

If B is 15% less than D.

17y = D of (100-15)%

17y = D of 85%

$$17y=D\times\frac{85}{100}$$

$$y=D\times\frac{5}{100}$$
$$y=D\times\frac{1}{20}$$
D = 20y

Let's assume that C is 'z' percentage of D.

C = z% of D

10y = z% of 20y

$$10y=z\times\frac{20y}{100}$$

$$1=z\times\frac{1}{50}$$

z = 50%

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