Question

The sum of two numbers is 40 and their difference
is 4. The ratio of the numbers is
(a) 11:9
(b) 11:18
(C) 21 : 19
(d) 22:9​

Answer 1

$\sf \green{ \underline{answer \ : option\: (a )}}$

Answer 2

AnswEr :

GivEn :

• Sum of 2 no. = 40
• Diff. of 2 no. = 4

To find :

• Ratio of numbers = ??

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• let's assume that the no.'s be x and y

$\implies$ x + y = 40 ---- ( i )

⠀⠀⠀⠀

$\implies$ x - y = 4 ------ ( ii )

⠀⠀⠀⠀

• Adding both the equations

⠀⠀⠀⠀

$\implies$ x + y + x - y = 40 + 4

⠀⠀⠀⠀

$\implies$ 2x = 44

⠀⠀⠀⠀

$\implies$ x = 22

⠀⠀⠀⠀

• Putting value of x in eq ( i )

$\implies$ x + y = 40

⠀⠀⠀⠀

$\implies$ 22 + y = 40

⠀⠀⠀⠀

$\implies$ y = 40 - 22

⠀⠀⠀⠀

$\implies$ y = 18

⠀⠀⠀⠀

• Ratio of numbers x : y

$\implies$ $\sf{\bold{\dfrac{x}{y} = \dfrac{22}{18}}}$

⠀⠀⠀⠀

$\implies$ $\sf{\bold{\dfrac{x}{y} = \dfrac{11}{9}}}$

Therefore,

• Ratio = 11 : 9 = option A