Question

Two numbers are in the ratio 3:5. When each of these numbers is increased by 10, their ratio becomes 5:7. Find the greater number. Please no spam tomorrow is my exam

Answer 1

Given:-

• Ratio = 3 : 5
• When Each number is increased by 10, the ratio = 5 : 7

━━━━━━━━━━━━━━━━

Need to find:-

• Greater number = ?

━━━━━━━━━━━━━━━━

Solution:-

Let the two numbers be:-

• 3x and
• 5x

Now when 3x is increased by 10:

→ New number = 3x + 10

When 5x is increased by 10:

→ New number = 5x + 10

Ratio of New numbers:-

→$\dfrac{3x + 10}{5x + 10}$

But, given that ratio = 5 : 7

Thus,

→$\dfrac{3x + 10}{5x + 10} = \dfrac{5}{7}$

→$7(3x + 10) = 5(5x + 10)$

→$21x + 70 = 25x + 50$

→$25x - 21x = 70 - 50$

→$4x = 20$

→$x = 20 \div 4$

→$\purple{\boxed {\bold{x = 5}}}$

━━━━━━━━━━━━

Clearly 5x > 3x

Thus the greater number is:-

= 5x

= 5 × 5

= 25

Therefore the $\red{\boxed {\bold{\large{Greater\:Number\:is\:25}}}}$

Answer 2

$\red{\textbf{Answer}}$ ➧ 25

Step-by-step explanation:

$\blue{\texttt{Given :-}}$

$\textsf{Two numbers are in the ratio 3:5}$

$\textsf{Let the first number is}$ $\blue{\texttt{x}}$

$\textsf{ the second number is}$ $\blue{\texttt{y}}$

$\textsf{then ,}$

$\Large\frac{x}{y} = \Large\frac{3}{5}$

$3y = 5x$

$\textsf{on the other hand,}$

$\Large\frac{x + 10}{y + 10} = \Large\frac{5}{7}$

$\textsf{hence,}$$7(x + 10) = 5(y + 10)$

$\textsf{we get that,}$

$3y = 5x$,$7x + 70 = 5y + 50$

$3y = 5x \: , 5y = 7x + 20$

$y = \Large\frac{5x}{3}$,$y = \Large\frac{7x + 20}{5}$

∴ $\Large\frac{5x}{3} = \Large\frac{7x + 20}{5}$

$25x = 3(7x + 20)$

$25x = 21x + 60$

$4x = 60$

∴ $x = 15$

$\textsf{then,}$

$y = \Large\frac{5x}{3} = 5 \times \Large\frac{15}{3}$ $= 25$

$\red{\textbf{x = 15 , y = 25}}$

$\blue{\texttt{The greater number is }}$ $\red{\textbf{25}}$