Question

If 10% of (A + B) = 50% of (A-B), then A : B=P: Q, then P+Q=​

Answer 1

Step-by-step explanation:

${Given: \: 10\%of \: (A + B) = 50\% \: of \: (A - B) \: and \: A:B = P:Q ,} \\ {to \: find \: P + Q \: .} \\ \tt:{ \implies{ \frac{10 \times (A+ B)}{100} = \frac{50 \times (A - B)}{100}.}} \\ {After \:common \: term \: cancellation \: it \: will \: be:} \\ {A + B = 5A - 5B.} \\ \tt:{ \implies{4A = 6B, \: \: \frac{A}{B} = \frac{6}{4}, \: \: A:B = 3:2.}} \\ {And \: it \: is \: given: \: A:B = P:Q.} \\ \therefore{P:Q = 3:2 \: suppose, \: P = 3x \: and \: Q = 2x \: then \:( P + Q) = 5x.} \\ \red{ \boxed{Where \: x \: is \: constant}} \\ {Or, \: we \:a lso \:conclude \: as, \frac{P}{Q} = \frac{3}{2}} \\ \tt:{ \implies{2P = 3Q,\: 2P + 2Q = 3Q + 2P, \: (P + Q) = \frac{3Q+ 2P}{2}. }}$