Akbar sets off on his car from Delhi to Jaipur at a certain speed intending to reach Jaipur by 5pm. After covering a certain distance, he realises that he would be able to cover only five – eighth of the intended distance by 5pm. He therefore increases his speed by 75 percent and reaches Jaipur at 5pm. What fraction of the total distance did he cover at his initial speed?

Correct Option - 2


Detailed Solution:

Let the distance between Delhi (D) and Jaipur (J) be 8x and Akbar’s initial speed be 4a and final speed be 7a.

Let the point where he increased his speed at P and let Q be the point on DJ such that $DP=\frac{5}{8}(DJ)$

$\frac{PQ}{PJ}=\frac{4}{7}$

Let PQ = 4y,

PJ = 7y

QJ = 7y – 4y = 3x

3y = 3x

y= x

PQ = 4x and PJ =7x

Required ratio = $\frac{DP}{DJ}$

= $\frac{x}{8x}$ = 1/8

<p>Let the distance between Delhi (D) and Jaipur (J) be 8x and Akbar’s initial speed be 4a and final speed be 7a.</p><p>Let the point where he increased his speed at P and let Q be the point on DJ such that&nbsp;<math><mrow><mi>D</mi><mi>P</mi><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo stretchy="false"> (</mo><mi>D</mi><mi>J</mi><mo stretchy="false">)</mo></mrow></math></p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754901417phpCpEFwk.jpeg" alt="" width="252" height="59" loading="lazy"></picture></div></div><p><math><mrow><mfrac><mrow><mi>P</mi><mi>Q</mi></mrow><mrow><mi>P</mi><mi>J</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>7</mn></mrow></mfrac></mrow></math></p><p>Let PQ = 4y, </p><p>PJ = 7y</p><p>QJ = 7y – 4y = 3x</p><p>3y = 3x</p><p>y= x</p><p>PQ = 4x and PJ =7x</p><p>Required ratio =&nbsp;<math><mrow><mfrac><mrow><mi>D</mi><mi>P</mi></mrow><mrow><mi>D</mi><mi>J</mi></mrow></mfrac></mrow></math></p><p>=&nbsp;<math><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mn>8</mn><mi>x</mi></mrow></mfrac></mrow></math>&nbsp;= 1/8</p>

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