Question

2 numbers are in the ratio 5:6 if 20 is added to each of them the ratio becomes 7:8 the number are​

Answer 1

Given :

• The Numbers are in the ratio 5:6
• If 20 is added to them they become 7:8

To Find :

• Find the Numbers

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN : We will form the Equation for this question by assuming the ratios as 5y and 6y .After Cross Multiplying, we can get the value of y .And can calculate the Numbers .Let's Solve :

$\dag$ Calculating the Value of y :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{First \; No.}{Second \; No.} \bigg\} = \bigg\{ \dfrac{5y}{6y} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{5y + 20}{6y + 20} \bigg\} = \bigg\{ \dfrac{7}{8} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 8 \bigg( 5y + 20 \bigg) = 7 \bigg( 6y + 20 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 40y + 160 = 42y + 140 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 42y - 40y = 160 - 140 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2y = 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { y = \dfrac{20}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { y = \cancel\dfrac{20}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\purple{\pmb{\frak { y = 10 }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Numbers :

• First No. = 5y = 5(10) = 50
• Second No. = 6y = 6(10) = 60

$\therefore \;$ The two numbers are 50 and 60 .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

Answer:

The two numbers are 50 and 60

Step-by-step explanation:

Given data the ratio of the 2 numbers = 5:6

after adding 20 to each of them the ratio becomes 7:8

Let 5x and 6x are be the 2 numbers [ ∵ both numbers are in 5:6 ratio]

after adding 20 the ratio of 2 numbers = 7:8

⇒  5x+20 : 6x+20 = 7:8

⇒  $\frac{ (5x+20)}{(6x+20)} = \frac{7}{8}$  

      8(5x+20) = 7(6x+20)

     40x + 160 = 42x + 140

     42x - 40x = 160 - 140

                 2x = 20

                   x = 10

the two numbers are    5x = 5(10) = 50        

                                      6x = 6(10) = 60