Question

Subtract the square of m from the ratio of p and q​

Answer 1

Answer:

P and Q are two numbers such that p>q. When you subtract 5 from p and subtract 5 from q, the answers are in the ratio 5:1. When you add 20 to p and add 20 to q, the answers are in the ratio 5:2. What is the ratio of p:q in its simplest form?

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Given (p-5)/(q-5) = 5/1 ……… (1)

further (p+20)/(q+20) = 5/2 ………. (2)

From (1) we get p-5 = 5(q-5) =5q - 25 => p = 5q -25+5 = 5q -20

Substituting p = 5q - 20 in (2) we get (5q-20+20)/(q+20) =5/2

=> 5q/(q+20) = 5/2 => q / (q+20) = 1/2 => 2q = q + 20 on cross multiplication

=> 2q -q = 20 = > q = 20

but we got p = 5q - 20 , on substituting q =20 , here

we get p = 5*20 -20 = 100 - 20 = 80

So, we got p = 80 and q = 20

Check (p-5)/(q-5) = (80 - 5) / ( 20 -5) = 75/15 =5 …. (correct)

further (p+20)/(q+20) = (80 + 20 ) / (20 + 20) = 100/40 = 5/2 … (correct)

It is verified also that p = 80 and q = 20 are correct answers. Therefore P:Q :: 4:1