Question

What number must be added to each of the numbers 25,35,40,55 , so that new numbers
are in proportion?​

Answer 1

$\star \: \large{\underline{\bf{Question-}}}$

• What number must be added to each of the numbers 25, 35, 49, 55 so that new numbers are in proportion.

$\star \: \large{\underline{\bf{Solution-}}}$

$\dashrightarrow\bf{25 + x : 35 + x : :40 + x : 55 + x} \\ \\ \dashrightarrow\bf{(25 + x)(55 + x) = (35 + x)(40 + x)} \\ \\ \dashrightarrow\bf{(25 \times 55) + 25x + 55x + {x}^{2} = (35 \times 40) + 35x + 40x + {x}^{2} } \\ \\ \dashrightarrow\bf{1375 + 25x + 55x + {\cancel{ {x}^{2} }= 1400 + 35x + 40x + {\cancel{ {x}^{2} }}}} \\ \\ \dashrightarrow\bf{1375 + 80x = 1400 + 75x} \\ \\ \dashrightarrow\bf{80x - 75x = 1400 - 1375} \\ \\ \dashrightarrow\bf{5x = 25} \\ \\ \dashrightarrow\bf{x = \dfrac{\cancel{25}}{\cancel{5}}} \\ \\ \dashrightarrow \boxed{\bf{\red{x = 5}}} \: \bigstar$

Therefore;

• 5 must be added to each of the numbers 25, 35, 40 and 55 so that new numbers will be in proportion.

Answer 2

Answer:

5

Step-by-step explanation:

25 35 40 55

25+x:35+x::40+x:55+x

(25+x)(35+x)=(35+x)(40+x)

1375+25x+55x+x

2

=1400+35x+40x+x

2

1375+80x=1400+75x

5x=25

x=5