Question

three no.s 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 no.s​

Answer 1

$\large\bf\underline{Given:-}$

• Ratio of three numbers is 4 :5 :6
• Sum of largest and smallest no = sum of third and 55

$\large\bf\underline {To \: find:-}$

• Numbers

$\huge\bf\underline{Solution:-}$

• Ratio of Numbers = 4:5:6

↱ Let the numbers be 4x , 5x and 6x

↬ According to Question:-

sum of the largest and the smallest equals the sum of the third and 55.

• Larger number = 6x
• smaller number = 4x
• third number = 5x

↣ 6x + 4x = 5x + 55

↣10x = 5x + 55

↣10x - 5x = 55

↣5x = 55

↣x = 55/5

↣ x = 11

✝ Three numbers are :-

↣4x = 4 × 11 = 44

↣5x = 5 × 11 = 55

↣6x = 6 × 11 = 66

♢ Three numbers are = 44, 55, and 66

$\rule{200}3$

Answer 2

$\sf\large{\underline{\underline{Question:-}}}$

three no.s 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 numbers.

$\sf\large{\underline{\underline{Given:-}}}$

• Three no. are in ratio = 4:5:6
• Sum of largest and the smallest equals the sum of the 3rd number.
• Largest number is = 6
• Smallest number is = 4
• 3rd number is = 5

$\sf\large{\underline{\underline{To\:Find:-}}}$

• Number=?

$\sf\large{\underline{\underline{According\: to \:question:-}}}$

Let all the ratios be in the form of x

So,

$\sf→ 4x+6x= 5x+55\\\sf→ 10x-5x=55\\\sf→ 5x=55\\\sf→ x=\frac{55}{5}=11\\\sf{\red{\fbox{\underline{\purple{X=11}}}}}$

$\sf\large{\underline{\underline{Hence:-}}}$

Putting x=11 in the given ratios.

☛4x= 4×11 = 44 (1st number)

☛5x = 5×11= 55 (2nd number)

☛6x= 6×11 = 66 (3rd number)