Question

5 773
6. The ages of Manu and Anu are in the
ages will be 77 years. What are their present ages
Manu and Anu are in the ratio of 4:9. Six years later, the sum of their​

Answer 1

Answer:

${\boxed{\bold{Present\:age\:of\:Manu =20\:years }}}$

${\boxed{\bold{Present\:age\:of\:Anu =45\:years}}}$

Step-by-step explanation:

Correct question:-

The ages of Manu and Anu are in the ratio of 4 : 9 . Six years later, the sum of their ages will be 77 years. What are their present ages?

$\bf{Given}\begin{cases}\sf {Ratio\:of\:their\:ages= 4 : 9}\\\sf {Sum\:of\:ages\:after\:6\:years = 77\:years}\\\sf{Present\:ages\:of\:them=?}\end{cases}$

Let the present age of Manu be 4x years and present age of Anu be 9x years.

$\tt After\:6\:years,\\\rm Manu's\:age\:will\:be = (4x + 6)\:years.\\\rm Anu's \:age\:will\:be = (9x + 6)\:years.$

$\bold{According\:to\:question\:now:-}$

$\rm (4x + 6) + (9x + 6) = 77 \\\rightarrow\rm 4x + 6 + 9x + 6 = 77 \\\rightarrow\rm 13x + 12 = 77 \\\rightarrow\rm 13x = 77 - 12 \\\rightarrow\rm 13x = 65 \\\rightarrow\rm x =\frac{65}{13}\: years \\\rightarrow{\boxed{\rm{ x = 5 \: years.}}}$

$\tt Now,$

$\leadsto\rm Present\:age\:of\:Manu = 4x =4(5) = 20\:years. \\\leadsto\rm Present \:age \:of\: Anu = 9x = 9(5) = 45 \:years.$

$\therefore\bold{\underline{Present\:age\:of\:Manu = 20\:years.}} \\\therefore\bold{\underline{Present\:age\:of\:Anu=45\:years.}}$

Answer 2

Correct Question:

The ages of Manu and Anu are in the ratio of 4 : 9 . Six years later, the sum of their ages will be 77 years. What are their present ages?

Answer:

Let the present ages of Manu and Anu be 4x and 9x respectively.

6 years hence,

Manu's age = (4x + 6) years

Anu's age = (9x + 6) years

WRQ,

$(4x + 6) + (9x + 6) = 77\\\\13x + 12 = 77\\\\13x = 65\\\\\boxed{x = 5}$

Hence, Present age of Manu = 4x = 4*5 = 20 years

Present age of Anu = 9x = 9*5 = 45 years