Question

Two numbers are in the ratio 3 : 4; if 6 be added to each terms of the ratio, then the new ratio will be 4:5, then the numbers are​

Answer 1

Given:

• Two numbers are in the ratio of 3:4
• 6 is added to each terms of the ratio
• New ratio is 4:5

To Find:

• The new numbers

Solution:

• Let the numbers be 3x and 4x.

New numbers :

$\mapsto \sf{ 3x + 6}$

$\mapsto \sf{ 4x + 6}$

• According to the question,

$\displaystyle{ :\implies \sf{ \frac{3x + 6}{4x + 6} = \frac{4}{5} }}$

• Cross Multiply

$\begin{gathered}{ : \implies \sf{5(3x + 6) = 4(4x + 6)}} \\ { : \implies \sf{16x + 24 = 15x + 30}} \\ { : \implies \sf{16x - 15x = 30 - 24}} \\:\implies \underline{\boxed{\frak{x = 6}}} \: \pink{ \bigstar}\end{gathered}$

• Hence, the Value of x is 6.

New numbers are :

• 1st number = 3x = 3 × 6 = 18
• 2nd number = 4x = 4 × 6 = 24

$\blue \bigstar\boxed{\sf{The \: new \: numbers \: are  18 and 24.}}$

Thank you!

@itzshivani