Question

Present ages of Rekha and Reshma are in ratio of 3:4. Five years from now the ratio of their ages will be 4:5.Find their present ages.

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Answer 1

Present age of Rekha be "3M" and present age of Reshma be "4M" years.

After five years, the ratio of their ages will be 4:5.

Now,

• Age od Rekha = (3M + 5) years
• Age of Reshma = (4M + 5) years

According to question,

=> (3M + 5)/(4M + 5) = 4/5

Cross multiply them

=> 5(3M + 5) = 4(4M + 5)

=> 15M + 25 = 16M + 20

=> 15M - 16M = 20 - 25

=> - M = - 5

=> M = 5

So,

Present age of Rekha = 3M

=> 3(5)

=> 15 years

Present age of Reshma = 4M

=> 4(5)

=> 20 years

Answer 2

Answer:

${\bold{\therefore Present\:age\:of\:Rekha=15\:years }}$

${\bold{\therefore Present\:age\:of\:Reshma=20\:years }}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about relation between ages of Rekha and Reshma.

• We have to find the present age of both Rekha and Reshma.

$\underline \bold{Given : } \\ \implies Present \: age \: ratio = 3 : 4 \\ \implies After \: 5 \: years \: ratio = 4 : 5 \\ \implies Let \: Present \: age \: of \: rekha = 3x \\ \implies Present \:age \: of \: reshma = 4x \\ \\ \underline \bold{To \: Find : } \\ \implies Present \: age \: of \: Rekha = ? \\ \implies Present \: age \: of \: Reshma = ?$

• According to given question :

$\bold{After \: 5 \: years} \\ \implies \frac{Present \: age \: of \: rekha + 5}{Present \: age \:o f \: reshma + 5} = \frac{4}{5} \\ \implies \frac{3x + 5}{4x + 5} = \frac{4}{5} \\ \bold{ Cross \: multipling\:both\:side: } \\ \implies (3x + 5)5 = 4(4x + 5) \\ \implies 15x + 25 = 16x + 20 \\ \implies 15x - 16x = 20 - 25 \\ \implies - x = - 5 \\ \bold{\implies x = 5} \\ \\ \bold{\therefore Present \: age \: of \: Rekha = 3x = 15 \: years} \\ \bold{\therefore Present \: age \: of \: Reshma = 4x = 20 \: years}$