(1) If the same number be added to the numbers 2, 4, 14 and 22 then the resultant numbers are in proportion. Find the number.
Answers
Answer:
1) Given:
If a number is added to 2 , 4 , 14 , 22 then the resultant numbers are in proportion.
Let the number be x.
So,
The resulting numbers are :
(2 + x) , (4 + x) , (14 + x) , (22 + x).
Now,
These numbers are in proportion.
we know that,
if four numbers/quantities or numbers are in proportion , then product of first quantity & second quantity is equal to the product of second and third quantities.
That is;
Product of extremes = Product of means.
So,
⟹ (2 + x)(22 + x) = (4 + x)(14 + x)
⟹ 2(22 + x) + X(22 + x) = 4(14 + x) + X (14 + x)
⟹ 44 + 2x + 22x + x² = 56 + 4x + 14x + x²
⟹ 24x + 44 = 18x + 56
⟹ 24x - 18x = 56 - 44
⟹ 6x = 12
⟹ x = 12/6
⟹ x = 2
∴ The required number is 2.
_________________________________
2) Let the number which is added be a.
Given:
If a is added to 25 , 7 , 1 ; the product of the first and third results is equal to the square of the second.
i.e.,
(25 + a)(1 + a) = (7 + a)²
(a + b)² = a² + b² + 2ab
⟹ 25(1 + a) + a(1 + a) = (7)² + (a)² + 14a
⟹ 25 + 25a + a + a² = 49 + a² + 14a
⟹ 26a + 25 = 14a + 49
⟹ 26a - 14a = 49 - 25
⟹ 12a = 24
⟹ a = 24/12
⟹ a = 2
∴ The number that is added is 2.
Step-by-step explanation:
thats just math
Answer:
4+x:7+x=14+x:22+x
⇒7+x4+x=22+x14+x
⇒(4+x)(22+x)=(7+x)(14+x)
⇒x2+26x+88=x2+21x+98
⇒5x=10
⇒x=2