Question

Three numbers are in the ratio 4:56If the sum of the largest and thesmallest equals the sum of the third and55. Find the on number​

Answer 1

Question :

• Three numbers are in the ratio 4:5:6. If the sum of the largest and the smallest equals the sum of the third and 55. Find the nnumber's.

Answer :

The numbers are 66, 55, 44 respectively.

Explanation :

Given,

• Ratio between three numbers = 4:5:6

• Sum of largest and smallest numbers = sum of third number + 55

Solution :

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

=> Largest number = 6x

=> Smallest number = 4x

Now, According to the question :

$6x + 4x = 5x + 55$

$10x = 5x + 55$

$10x - 5x = 55$

$5x = 55$

$x = \frac{55}{5}$

$x = \cancel \frac{55}{5}$

$x = 11$

Therefore, the value of x is 11.

• Now greatest number = 6x = 6 × 11 = 66

• Smallest number = 4x = 4 × 11 = 44

• Third number = 5x = 5 × 11 = 55.

Therefore, the numbers are 66, 55, 44 respectively.

Answer 2

Solution :-

Given That, Three numbers are in the ratio 4: 5 :6.

Lets Assume That, These Numbers are 4x, 5x & 6x .

So,

→ Smallest Number = 4x .

→ Largest Number = 6x .

A/q,

→ Smallest Number + Largest Number = Third Number + 55 .

→ 4x + 6x = 55 + 5x

→ 10x - 5x = 55

→ 5x = 55

Dividing Both sides by 5,

→ x = 11.

Hence,

→ Smallest Number = 4x = 4*11 = 44(Ans).

→ Largest Number = 6x = 6*11 = 66 (Ans).

→ Third Number = 5x = 5*11 = 55 (Ans).