Question

Two number are in the ratio 3:4 if 8 is added to each number they became in the ratio 4:5 find the number

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given two numbers are in ratio 3:4
• When 8 is added to both the numbers they became in ratio 4:5

To Find:

• We have to find both numbers

Solution:

Let First number = 3x

Second number = 4x

_______________________________

$\bigstar \: \: \underline{\large\mathfrak\orange{According \: to \: the \: Question:}}$

When 8 is added to both the numbers they became in ratio 4:5

$\hookrightarrow \sf{\dfrac{3x+8}{4x+8} = \dfrac{4}{5} }$

Cross Multiplying the Terms

$\hookrightarrow \sf{5(3x+8)=4(4x+8)}$

$\hookrightarrow \sf{15x + 40 =16x+32}$

$\hookrightarrow \sf{16x-15x=40-32}$

$\hookrightarrow \boxed{\sf{x=8}}$

________________________________

Hence the number are

$\implies \sf{First \: number = 3x }$

$\implies \sf{3 \times 8}$

$\implies \sf{24 }$

$\implies \sf{Second \: number = 4x}$

$\implies \sf{ 4 \times 8}$

$\implies \sf{32}$

$\boxed{\large\mathfrak\red{First \: number = 24}}$

$\boxed{\large\mathfrak\red{Second \: number = 32}}$

________________________________

$\huge\mathfrak\green{Verification:}$

1) Numbers are in ratio 3:4

$\implies \sf{Ratio = \dfrac{24}{32} = \dfrac{3}{4} }$

2) When 8 is added to both numbers their ratio becomes 4:5

$\implies \sf{Ratio = \dfrac{24 + 8}{32 + 8}}$

$\implies \sf{Ratio = \dfrac{32}{40}}$

$\implies \sf{Ratio = \dfrac{4}{5}}$

Hence Verified !!

Answer 2

Answer:

Given:

We have been given two numbers are in ratio 3:4

When 8 is added to both the numbers they became in ratio 4:5

To Find:

We have to find both numbers

Solution:

Let First number = 3x

Second number = 4x

_______________________________

\bigstar \: \: \underline{\large\mathfrak\orange{According \: to \: the \: Question:}}★

AccordingtotheQuestion:

When 8 is added to both the numbers they became in ratio 4:5

\hookrightarrow \sf{\dfrac{3x+8}{4x+8} = \dfrac{4}{5} }↪

4x+8

3x+8

=

5

4

Cross Multiplying the Terms

\hookrightarrow \sf{5(3x+8)=4(4x+8)}↪5(3x+8)=4(4x+8)

\hookrightarrow \sf{15x + 40 =16x+32}↪15x+40=16x+32

\hookrightarrow \sf{16x-15x=40-32}↪16x−15x=40−32

\hookrightarrow \boxed{\sf{x=8}}↪

x=8

________________________________

Hence the number are

\implies \sf{First \: number = 3x }⟹Firstnumber=3x

\implies \sf{3 \times 8}⟹3×8

\begin{lgathered}\implies \sf{24 } \\\end{lgathered}

⟹24

\implies \sf{Second \: number = 4x}⟹Secondnumber=4x

\implies \sf{ 4 \times 8}⟹4×8

\begin{lgathered}\implies \sf{32} \\\end{lgathered}

⟹32

\begin{lgathered}\boxed{\large\mathfrak\red{First \: number = 24}} \\\end{lgathered}

Firstnumber=24

\begin{lgathered}\boxed{\large\mathfrak\red{Second \: number = 32}} \\\end{lgathered}

Secondnumber=32

________________________________

\huge\mathfrak\green{Verification:}Verification:

1) Numbers are in ratio 3:4

\begin{lgathered}\implies \sf{Ratio = \dfrac{24}{32} = \dfrac{3}{4} } \\\end{lgathered}

⟹Ratio=

32

24

=

4

3

2) When 8 is added to both numbers their ratio becomes 4:5

\implies \sf{Ratio = \dfrac{24 + 8}{32 + 8}}⟹Ratio=

32+8

24+8

\implies \sf{Ratio = \dfrac{32}{40}}⟹Ratio=

40

32

\begin{lgathered}\implies \sf{Ratio = \dfrac{4}{5}} \\\end{lgathered}

⟹Ratio=

5

4