Question

the ages of hari and harry are in ratio of 5;7 . four years from now the ratio of their ages will be 3;4 .find their present ages

Answer 1

Answer :

• Present age of Hari = 20 years
• Present age of Harry = 28 years

Given :

• The ages of Hari and Harry are in the ratio of 5 : 7
• Four years from now the ratio of ages will be 3 : 4

To find :

• Present ages

Solution :

Given

The ages of Hari and Harry are in the ratio of 5 : 7 so,

• Let the age of Hari be 5x
• Let the age of Harry be 7x

According to question :

Four years from now the ratio of their ages will be 3 : 4 so,

• 5x + 4 / 7x + 4 = 3/4

➠ 5x + 4 / 7x + 4 = 3/4

➠ 4(5x + 4) = 3(7x + 4)

➠ 20x + 16 = 21x + 12

➠ 20x - 21x = 12 - 16

➠ -x = -4

➠ x = 4

• Hari age = 5x = 5(4) = 20 years
• Harry age = 7x = 7(4) = 28 years

Hence,

• Present age of Hari = 20 years
• Present age of Harry = 28 years

Verification :

➠ 5x + 4 / 7x + 4 = 3/4

➠ 5(4) + 4 / 7(4) + 4 = 3/4

➠ 20 + 4 / 28 + 4 = 3/4

➠ 24/32 = 3/4

➠ 3/4 = 3/4

Hence , Verified

Answer 2

Gɪᴠᴇɴ :

• The ages of hari and Harry are in ratio of 5 : 7.

• After 4 years their ratio will be 3 : 4.

Tᴏ ғɪɴᴅ :

• Find their present ages..!!

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$\begin{gathered} \sf \: let \: the \: common \: number \: be \: x. \\ \\ \sf \therefore \: Hari's \: age = 5x \\ </p><p> \sf \: \: \: \: \: \: \: Harry's \: age = 7x \\ \\ \\ \;\;\;\;\bf{\dag}\;{\underline{\sf{ \pmb{According \: to \: condition }}}} \\ \\ \sf After \: four \: years, \\ \\ \sf \: Hari's \: age = 5x + 4 \\ \sf \: Harry's \: age = 7x + 4 \\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \therefore \: \:\rightarrow \underline{ \boxed{ \sf{ \frac{5x + 4}{7x + 4} = \frac{3}{4}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \sf\: 4(5x + 4) = 3(7x + 4) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \sf \: 20x + 16 = 21x + 12 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \sf \: 16 - 12 = 21x - 20x \\ \\ \dashrightarrow\underline{ \boxed{ \tt \color{pink}{x = 4}}} \end{gathered}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━$

$\;\;\;\;\bf{\dag}\;{\underline{\sf{ \pmb{Substitute \: the \: value \: of \: x }}}}$

$\begin{gathered} \sf \dag \: \: \: \: Hari's \: age = 5x = 5 \times 4 = 20 \\ \\ </p><p> \sf \: \dag \: \: \: \: \: Harry's \: age = 7x = 7 \times 4 = 28 \end{gathered}$