Question

. Three numbers are in the ratio of 4:5: 6. If the sum of the largest and the smallest equals
the sum of the third and 55, find the numbers.​

Answer 1

Step-by-step explanation:

Given that the three numbers are in the ratio 4:5:6.

Let the three numbers be 4x,5x and 6x respectively.

Now,

According to the question-

6x+4x=5x+55

10x−5x=55

⇒x=

5

55

=11

Therefore,

First no. =4×11=44

Second no. =5×11=55

Third no. =6×11=66

Hence the three numbers are 44,55 and 66.

Answer 2

Given three number which are in ratio 4:5:6.

So, Let the numbers be 4x, 5x and 6x.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

☯ Sum of largest and smallest no. is equals to the sum of third and 55.

${\frak{Here}} \begin{cases} & \text{Smallest number = \bf{4x} } \\ & \text{Largest number = \bf{6x} } \\ & \text{Remaining third number = \bf{5x} } \end{cases}$

Therefore,

$:\implies\sf 4x + 6x = 5x + 55$

$\qquad:\implies\sf 10x = 5x + 55$

$\qquad:\implies\sf 10x - 5x = 55$

$\qquad\quad:\implies\sf 5x = 55$

$\qquad\quad:\implies\sf x = \cancel{ \dfrac{55}{5}}$

$\qquad\quad:\implies{\underline{\boxed{\frak{\purple{x = 11}}}}}\;\bigstar$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☯ Therefore, Required numbers are,

• 4x = 4 × 11 = 44

• 5x = 5 × 11 = 55

• 6x = 6 × 11 = 66

Where,

44 is the smallest number and 55 is the largest number.