Atul decided to distribute gold coins to his three sons in the following way 2nd son would get $\frac{5}{7}$ of what the 1st son would get $\frac{3}{5}$ and the 3rd son would get set of what the 2nd son would get. 1st son got 60 gold coins more than the 3rd son. How many gold coins were distributed to the three sons?

<p>Let y gold coins were given to 1st son.</p><p>Number of gold coins given to 2nd son =&nbsp;<math><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mi>y</mi></mrow></math></p><p>Number of gold coins given to 3rd son =&nbsp;<math><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mi>y</mi></mrow></math></p><p>So, &nbsp;<math><mrow><mi>y</mi><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mi>y</mi><mo>=</mo><mn>6</mn><mn>0</mn><mtext> </mtext><mtext> </mtext><mo>⇒</mo><mtext> </mtext><mtext> </mtext><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>7</mn></mrow></mfrac><mo>=</mo><mn>6</mn><mn>0</mn></mrow></math></p><p><math><mrow><mo>⇒</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>y</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mn>0</mn><mo>×</mo><mn>7</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mn>5</mn><mo>×</mo><mn>7</mn><mo>=</mo><mn>1</mn><mn>0</mn><mn>5</mn></mrow></math></p><p>Hence, the required number of gold coins:</p><p><math><mrow><mo>=</mo><mn>1</mn><mn>0</mn><mn>5</mn><mo>+</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mo>×</mo><mn>1</mn><mn>0</mn><mn>5</mn><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mo>×</mo><mn>1</mn><mn>0</mn><mn>5</mn></mrow></math></p><p>= 105 + 75 + 45 = 225</p>

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