Question

the ages of ram and sham are in the ratio 5:7.if ram is 9 years older and Shyam is 9 years younger. the age of ram would have been twice the age of Shyam .find their ages

Answer 1

Answer:

Ram is 15 yrs and shyam is 21 yrs

Step-by-step explanation:

5x+9=2(7x-9)

5x+9=14x-18

18+9=14x-5x

27=9x

x=3

ram=5x. shyam=7x

=15. =21

Hope it helped

Answer 2

$\sf\large\underline{Let:}$

• $\sf{The\:age\:of\: their\: ratio\:be\:x}$
• $\sf{The\:age\:of\:Ram=5x\: years}$
• $\sf{The\:age\:of\:Shayam=7x\: years}$

$\sf\large\underline{To\: Find:}$

• $\sf{The\:age\:Ram\:and\: Shayam=?}$

$\sf\large\underline{Solution:}$

• $\sf{Given,\:the\: ratio\:of\: their\:age=5:7}$
• $\sf{Ram\:is\:9ys\: older\:and\:shayam\:is\:9ys\:younger}$
• $\sf{The\:age\:of\:Ram\:is\: twice\:the\:age\:of\: Shayam}$

$\sf\large{As\:per\:the\: above\: information:}$

$\rm{\implies 5x+9=2(7x-9)}$

$\rm{\implies 5x+9=14x-18}$

$\rm{\implies 5x-14x=-18-9}$

$\rm{\implies -9x=-27}$

$\rm{\implies -9x=-27}$

$\rm\orange{\implies x=3}$

Hence,

$\rm\purple{\implies The\:age\:of\:Ram=5x=5*3=15year's}$

$\rm\green{\implies The\:age\:of\: shayam=7x=7*3=21year's}$

$\sf\large\underline{Verification:}$

$\rm{\implies 5x+9=2(7x-9)}$

$\rm{\implies 5*3+9=2(7*3-9)}$

$\rm{\implies 15+9=2(21-9)}$

$\rm{\implies 24=24}$

$\rm{\implies Ratio=\dfrac{Ram's\:age}{Shayam's\:age}=\dfrac{15}{21}=\dfrac{5}{7}}$

$\sf\large\underline{Hence,\: Verified:}$