Question

What is the difference between the present ages of ayush and deepak? i. the ratio between ayush's present age and his age after 8 years 4 : 5. ii. the ratio between the present ages of ayush and deepak is 4 : 3. iii. the ratio between deepak's present age and his age four years ago is 6 : 5.

a. any two of i, ii and iii?

Answer 1

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Answer 2

$i ) Present \:age \: of \: Ayush = x \: years$

$Ayush's \:age \: after \:8 \: years = (x+8) \:yrs$

/* According to the problem given */

$x : ( x + 8 ) = 4 : 5$

$\implies 5x = 4(x+8)$

$\implies 5x = 4x+ 32$

$\implies 5x - 4x = 32$

$\implies x = 32$

$\therefore Present \:age \: Ayush = 32 \:yrs$

$ii ) Let \: present \:age \:of \: Deepak = y \:yrs$

/* According to the problem given */

$32 : y = 4 : 3$

$\implies 4y = 3 \times 32$

$\implies y = \frac{3 \times 32}{4}$

$\implies y = 3 \times 8$

$\implies y = 24 \:yrs$

$Now, \red { The \ : differnce \: between \: the }\\\red{ present \: ages \:of \: Ayush \:and \: Deepak }\\ = 32 \:yrs - 24 \: yrs \\\green { = 8 \:yrs }$

$iii ) Ratio \: between \: Deepak's \: present \\age \: and \: his \: age \: four \: years \: ago \\= \frac{ 24 }{ 24 - 4 } \\= \frac{ 24 }{ 20 } \\\green { = \frac{ 6}{5} }\\= \green { 6 : 5 }$

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