y-is-varies-directly-as-the-square-of-x-and-inversely-as-z-if-x-is-inceased-by-10-and-z-is-decreased-by-20-find-the-percentage-change-in-y-

Question Number 57284 by Jmasanja last updated on 01/Apr/19

y i s v a r i e s d i r e c t l y a s t h e s q u a r e o f x a n d

i n v e r s e l y a s z .

i f x i s i n c e a s e d b y 10 % a n d z i s

d e c r e a s e d b y 20 %, f i n d t h e p e r c e n t a g e

c h a n g e i n y .

Commented by mr W last updated on 01/Apr/19

x_{2} = 1.1 x_{1}

z_{2} = 0.8 z_{1}

\frac{y_{2}}{y_{1}} = {(\frac{x_{2}}{x_{1}})}^{2} (\frac{z_{1}}{z_{2}}) = 1 . 1^{2} \times \frac{1}{0.8} = 1.5125

\Rightarrow y i s i n c r e a s e d b y 51 . 25 % .

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

y \propto x^{2}

y \propto \frac{1}{z}

c o m b i n i n g

y \propto \frac{x^{2}}{z} \to y = k \times \frac{x^{2}}{z}

l e t x c h a n g e s f r o m 100 \to 110

z c h a n g e s f r o m 100 \to 80

y_{1} = \frac{{k x}^{2}}{z}

y_{1} = \frac{k \times 100^{2}}{100} s o y_{1} = 100 k

n o w y_{2} = \frac{k \times 110^{2}}{80}

y_{2} = \frac{k \times 1210}{8}

△ y = y_{2} - y_{1} = \frac{1210 k}{8} - \frac{100 k}{1} = \frac{1210 k - 800 k}{8}

△ y = \frac{410 k}{8}

% i n c r e a s e o f y i s \frac{△ y}{y_{1}} \times 100

= \frac{410 k}{8 \times 100 k} \times 100

= \frac{410}{8} = 51 . 25 % i n c r e a s e