Question

The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.
A)

Answer 1

$Let\: x\: and\: y\: be\: the\: present \:ages \:of\: P\: and \:Q\: respectively.\\Then \:,\frac{x}{y} =\frac{3}{4} \\\:\:\:\:\:\:\:x = \frac{3y}{4} \\Five\: years\: ago ,\\Age\: of\: P = x-5\\Age \:of\: Q = y-5\\Then ,\\\frac{x-5}{y-5}=\frac{5}{7} \\\\\longrightarrow 7 (x-5) =5 (y-5)\\\\\longrightarrow7x-35 =5y-25\\\\\longrightarrow 7x-5y =10\\\\Substituting\: the\; value \:of\: x ,\\\longrightarrow7\times(\frac{3y}{4} )-5y=10\\\\\longrightarrow \frac{21y}{4} -5y = 10$

$\longrightarrow 21y - 20y = 40\\\\\longrightarrow y = 40$

$x =\frac{3y}{4} \\\\x = \frac{3\times40}{4} \\\\x = 30$

PRESENT AGE OF P = 30 YEARS

PRESENT AGE OF Q = 40 YEARS

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Answer 2

Answer:

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