A fraction $\frac{p}{q}$ $\frac{}{}$ is such that p, q > 0. If 3 is subtracted from the numerator fraction becomes –1. If 2 is added to denominator the fraction becomes $\frac{1}{4}$ $\frac{}{}$ . Find value of p & q respectively.

<p> (a): <span contenteditable="false"> <math> <mrow>As<mtext> </mtext><mtext> </mtext>given<mtext> </mtext><mtext> </mtext><mfrac><mrow><mi>p</mi><mo>−</mo><mn>3</mn></mrow><mrow><mi>q</mi></mrow></mfrac><mtext> </mtext><mo>=</mo><mtext> </mtext><mo>−</mo><mn>1</mn><mtext> </mtext><mo>⇒</mo><mtext> </mtext><mi>p</mi><mo>+</mo><mi>q</mi><mo>=</mo><mn>3</mn></mrow> </math> </span><math><mrow></mrow></math>&nbsp;. (1)</p><p><math><mrow></mrow></math><span contenteditable="false"> <math> <mrow>Also<mtext> </mtext><mtext> </mtext><mfrac><mrow><mi>p</mi></mrow><mrow><mi>q</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mtext> </mtext><mo>⇒</mo><mtext> </mtext><mn>4</mn><mi>p</mi><mo>−</mo><mi>q</mi><mo>=</mo><mn>2</mn></mrow> </math> </span>&nbsp;. (2)</p>

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