Question

Solve 20% of (P+Q)=50% of (P-Q), find P:Q = ?

Answer 1

Given :

20% of (P + Q) = 50% of (P - Q)

If we remove of, there comes a sign of multiplication ( × ) and if we remove %, the number will be divided by 100.

$\therefore$

$\dfrac{20}{100}$ × (P + Q) = $\dfrac{50}{100}$ × (P - Q)

$\dfrac{2{\cancel{0}}}{10{\cancel{0}}}$ × (P + Q) = $\dfrac{5{\cancel{0}}}{10{\cancel{0}}}$ × (P - Q)

$\dfrac{2}{10}$ × (P + Q) = $\dfrac{5}{10}$ × (P - Q)

$\dfrac{2}{{\cancel{10}}}$ × (P + Q) = $\dfrac{5}{{\cancel{10}}}$ × (P - Q)

2 (P + Q) = 5 (P - Q)

Open the ( ) brackets, we get

2P + 2Q = 5P - 5Q

2P - 5P = - 5Q - 2Q

- 3P = - 7Q

${\cancel{-}}$ 3P = ${\cancel{-}}$ 7Q

3P = 7Q

Rearranging it, we get

$\dfrac{P}{Q}$ = $\dfrac{7}{3}$

$\therefore$

P : Q = 7 : 3