Question

The respective ratio between the present ages of Ram, Rohan and Raj is 4:3:5. Ifthe average of their present ages is 36 years then what would be the sum of the ages of Ram and Rohan together after 7 years ?​

Answer 1

Answer:-

$\sf{The \ sum \ of \ the \ ages \ Ram \ and \ Rohan}$

$\sf{together \ after \ 7 \ years \ is \ 77 \ years.}$

Given:

• The respective ratio between the present ages of Ram, Rohan and Raj is 4:3:5.

• Average of their ages is 36 years.

To find:

• The sum of the ages of Ram and Rohan together after 7 years.

Solution:

$\sf{Let \ the \ constant \ be \ n.}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{\implies{Ram's \ age=4n}}$

$\sf{\implies{Rohan's \ age=3n}}$

$\sf{\implies{Raj's \ age=5n}}$

$\sf{According \ to \ the \ second \ condition.}$

$\boxed{\sf{Average=\frac{Sum \ of \ observations}{Number \ of \ observations}}}$

$\sf{\frac{4n+3n+5n}{3}=36}$

$\sf{\therefore{4n+3n+5n=36\times3}}$

$\sf{\therefore{12n=108}}$

$\sf{\therefore{n=\frac{108}{12}}}$

$\boxed{\sf{\therefore{n=9}}}$

$\sf{\therefore{Ram's \ age=4(9)=36 \ years,}}$

$\sf{Rohan's \ age=3(9)=27 \ years.}$

$\sf{\therefore{Ram's \ age \ after \ seven \ years=36+7}}$

$\sf{=43 \ years}$

$\sf{Rohan's \ age \ after \ seven \ years=27+7}$

$\sf{=34 \ years.}$

$\sf{Sum \ of \ the \ ages \ of \ Ram \ and \ Rohan}$

$\sf{after \ 7 \ years.=43+34=77 \ years.}$

$\sf\purple{\tt{\therefore{The \ sum \ of \ the \ ages \ Ram \ and \ Rohan}}}$

$\sf\purple{\tt{together \ after \ 7 \ years \ is \ 77 \ years.}}$

Answer 2

$\purple {\bf {\underline {We\:are\:given:-}}}$

▪The ratio between the present age of Ram, Rohan and raj is 4:3:5.

▪The average of their present age is 36

$\purple {\bf {\underline {We\:have\:to\:find:-}}}$

▪The sum of the ages of Ram, Rohan together after 7 years.

$\huge\purple {\bf {\underline {Solution:-}}}$

Here, Constant is 'n'.

✮ So, according to the 1ˢᵗ condition,

$\bold\blue{The\:sum\:of\:the\:Present\:Age\:of\:Ram,\:Rohan\:and\:Raj\:is=4n+3n+5n.}$

We know that,

$\pink{\boxed{Average=\frac{Sum\:of\:observation}{Number\:of\:the\:observation}}}$

$\bold\green{So,\:the\:average\:of\:there\:age\:is= \frac{4n + 3n + 5n}{3}}$

✮ So, according to the 2ⁿᵈ condition,

$\frac{4n + 3n + 5n}{3} = 36 \\ ⟹4n + 3n + 5n = 108 \\ ⟹12n = 108 \\ ⟹n = \frac{108}{12} \\ ∴ n = 9$

➽ Ram's age = 4 × 9 = 36

➽ Rohan's age = 3 × 9 = 27

➽ Raj's age = 5 × 9 = 45

✦ After 7 years Ram's age will be = 36 + 7 = 43

✦ After 7 years Rohan's age will be = 27 + 7 = 34

∴ After 7 years the sum Ram's and Rohan's age is = (43 + 34) = 77

$\bold\purple{\boxed {The\:Answer\:is\:77.}}$

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