Question

Practice to be Perfect 2.2
9 Three numbers are in the ratio of 4:5:6. If the sum of the largest and the smallest is equal to the twice of
55, find the numbers.​

Answer 1

The Numbers Are 44, 55 And 66 Respectively.

ExplanaTion:-

Given:-

• Three numbers are in ratio 4:5:6.

• Sum of the smallest and the largest number is twice of 55.

To Find:-

• The Numbers.

Now,

It is given that the three numbers are in ratio 4:5:6.

So let the numbers be 4x, 5x and 6x respectively.

Clearly we can see that 4x is the smallest number and 6x is the largest number.

So Acc. To. Que:-

↦ Smallest No. + Largest No. = 2 × 55.

↦ 4x + 6x = 110.

↦ 10x = 110.

↦ x = 110/10.

↦ x = 11.

We get the value of x which is 11.

So let us find out the numbers:-

↦ 4x = 4 × 11 = 44.

↦ 5x = 5 × 11 = 55.

↦ 6x = 6 × 11 = 66.

Therefore the numbers are 44, 55, 66 respectively.

VerificaTion:-

In the question it is given that sum of smallest number and largest number is twice of 55.

Here we can see that,

↦ 44 + 66 = 110...(1)

Also,

↦ Twice of 55 = 2 × 55 = 110...(2)

So eq(1) = eq(2).

...Hence Verified...

Answer 2

Correct Question:

Three numbers are in the ratio of 4:5:6. If the sum of the largest and the smallest is equal to the twice of  55, find the numbers.

Your Answer:

Given:-

• The numbers are in the ratio 4:5:6
• The sum of the largest and the smallest is equal to the twice of  55.

To find:-

• The numbers

Solution:-

$\tt Let\: the\: number\: be\: 4x,5x\: and\: 6x$

$\tt According \:to\: the\: Question\\\\\tt 4x+6x=2(55)$

Now solving the Equation for the values of x

$\tt 4x+6x=2(55)\\\\ \tt \Rightarrow\:\: 10x=110\\\\\Rightarrow\tt x=11\\\\\\\\ \tt So, the\:\: numbers\:\: are\\\\\tt 4x=4(11)=44\\\\ \tt 5x=5(11)=55\\\\ 6x=6(11)=66$

So the numbers are 44,55,66.