Question

2.
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

Answer :

• The numbers are 44 , 55 and 66

Given :

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

To find :

• The Numbers

Solution :

Given three numbers are in the ratio 4:5:6 so,

Let the ratio be 4x , 5x and 6x

According to question, Given that, the sum of the largest and the smallest equals the sum of the third and 55 then,

➨ 4x + 6x = 5x + 55

➨ 10x - 5x = 55

➨ 5x = 55

➨ x = 55/5

➨ x = 11

Now , we have to find the numbers :

➨ 4x = 4(11) = 44

➨ 5x = 5(11) = 55

➨ 6x = 6(11) = 66

Hence , The numbers are 44,55 and 66.

Answer 2

$\large \tt \green{ \underline{ Given: }}$

• Three numbers are in ratio of 4 : 5 : 6.

• The sum of the largest and the smallest equals to the sum of the third and 55

$\:$

$\large \tt \green{ \underline{To \: find : }}$

• Find the numbers

$\:$

$\large \tt \green{ \underline{Solution :}}$

$\sf{Let \: the \: common \: number \: be \: "x"}$

$\sf{ \therefore \: 4x,5x,6x}$

$\sf{The \: largest \: number \: and \: smallest \: number = 6x \: and \: 4x}$

$\sf{ \therefore \: Equation = \fbox{ \sf \pink{{4x + 6x = 5x + 55}}}}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \hookrightarrow \: 10x = 5x + 55}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \hookrightarrow \: 10x - 5x = 55}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \hookrightarrow \: 5x = 55}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \hookrightarrow \: x = \cancel \frac{55}{5} }$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \hookrightarrow \: x = 11}$

______________________________________________

$\sf{Number : 4x = 4 \times 11 = 44}$

$\sf{ \qquad \: \: \: \: \: \: \: \: 5x = 5 \times 11 = 55}$

$\sf{ \qquad \: \: \: \: \: \: \: \: 6x = 6 \times 11 = 66}$

$\sf{ \qquad \: \: \: \: \: \: \therefore { \underline{ Hence \: the \: numbers \: are \: 44,55,66}}}$