Verified answer

[tex]\bf Given:[/tex]

[tex] \sf \: Age \: of \: P = 25 years[/tex]

[tex] \sf \: Q \: is \: 5 \: years \: younger \: than \: R[/tex]

[tex] \sf \: Ratio \: of \: age \: of \: Q \: and \: R \: is \: 2 ∶ 3[/tex]

[tex] \sf \: Average \: age \: of \: all \: is \: 30 \: years[/tex]

[tex] \bf \: Formula \: used:[/tex]

[tex] \sf \: Average = \frac{Sum \: of \: all \: terms}{Total \: number \: of \: terms} [/tex]

[tex] \bf \: Calculation:[/tex]

[tex] \sf \: Let \: the \: ratio \: be \: x[/tex]

[tex] \sf \: 3x – 2x = 5[/tex]

[tex] \bf \implies x = 5 [/tex]

Age of Q = 2x = 2 × 5 = 10 years and Age of R = 3x = 3 × 5 = 15 years

Now, Average age of all four is 30 years

[tex] \sf \: Sum \: of \: age \: of \: all = 4 × 30 = 120 years[/tex]

[tex] \sf \: Age \: of \: S = 120 – (25 + 15 + 10) = 70 years[/tex]

∴ Ratio of age of R and S = 15 ∶ 70 = 3 ∶ 14

Step-by-step explanation:

Given:

\sf \: Age \: of \: P = 25 yearsAgeofP=25years

\sf \: Q \: is \: 5 \: years \: younger \: than \: RQis5yearsyoungerthanR

\sf \: Ratio \: of \: age \: of \: Q \: and \: R \: is \: 2 ∶ 3RatioofageofQandRis2∶3

\sf \: Average \: age \: of \: all \: is \: 30 \: yearsAverageageofallis30years

\bf \: Formula \: used:Formulaused:

\sf \: Average = \frac{Sum \: of \: all \: terms}{Total \: number \: of \: terms}Average=

Totalnumberofterms

Sumofallterms

\bf \: Calculation:Calculation:

\sf \: Let \: the \: ratio \: be \: xLettheratiobex

\sf \: 3x – 2x = 53x–2x=5

\bf \implies x = 5⟹x=5

Age of Q = 2x = 2 × 5 = 10 years and Age of R = 3x = 3 × 5 = 15 years

Now, Average age of all four is 30 years

\sf \: Sum \: of \: age \: of \: all = 4 × 30 = 120 yearsSumofageofall=4×30=120years

\sf \: Age \: of \: S = 120 – (25 + 15 + 10) = 70 yearsAgeofS=120–(25+15+10)=70years

∴ Ratio of age of R and S = 15 ∶ 70 = 3 ∶ 14