Question

If x,y is 20%,25% greater than z then how much percentage is x smaller than y?

Answer 1

SOLUTION

GIVEN

If x , y is 20%,25% greater than z respectively

TO DETERMINE

The percentage x smaller than y

EVALUATION

Here it is given that x is 20% greater than z

So

$\displaystyle \sf{x = \frac{120z}{100} \: }$

$\implies \displaystyle \sf{z= \frac{100x}{120} \: } \: \: ...(1)$

$\displaystyle \sf{y = \frac{125z}{100} \: }$

$\implies \displaystyle \sf{z= \frac{100y}{125} \: } \: \: .....(2)$

From Equation (1) & Equation (2) we get

$\displaystyle \sf{ \frac{100x}{120} = \frac{100y}{125} \: }$

$\implies \displaystyle \sf{ \frac{x}{120} = \frac{y}{125} \: }$

$\implies \displaystyle \sf{ \frac{x}{24} = \frac{y}{25} \: }$

$\implies \displaystyle \sf{ x = \frac{24y}{25} \: }$

$\implies \displaystyle \sf{ y - x = y - \frac{24y}{25} \: }$

$\implies \displaystyle \sf{ y - x = \frac{y}{25} \: }$

$\implies \displaystyle \sf{ y - x = \frac{y}{25} \times 100 \% }$

$\implies \displaystyle \sf{ y - x = y \times 4 \% }$

Hence x is smaller than y by 4%

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LEARN MORE FROM BRAINLY

The angles of the triangle

are 3x–40, x+20 and 2x–10

then the value of x is

(a) 40 (b) 35 (c) 50 (d) 45

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