Question

Two numbers are in the ratio of 5:6. If 5 is added to both the numbers the new ratio will be 6:7. Find the two numbers.numbers. . . What is its solutin
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Answer 1

Answer:

let the no. be 5x and 7x

it means that 5x+5/6x+5 =6/7

7 (5x+5)=6 (6x+5)

35x +35=36x+30

35x-36x=30-35

-x=-5

x=5

so no.=7×5=35

and5×5=25

Answer 2

$\bf{\underline{\huge{\boxed{\sf{\green{Answer:}}}}}}$

$\bf{\underline{\underline{\rm{\blue{Given:}}}}}$

• Two numbers are in the ratio of 5:6
• If 5 is added to both the numbers the new ratio will be 6:7

$\bf{\underline{\underline{\rm{\blue{To\:find:}}}}}$

• The two numbers

$\bf{\underline{\underline{\rm{\blue{Solution:}}}}}$

Let x be the common multiple of the ratio 5:6

•°• Small number = 5x

Greater number = 6x

$\bf{\underline{\underline{\rm{\green{According\:to\:question:}}}}}$

• If 5 is added to both the numbers the new ratio will be 6:7

Smaller number = 5x + 5

Greater number = 6x + 5

Ratio = 6:7

Representing the condition mathematically,

=> $\large\frac{5x+5}{6x+5}$ = $\large\frac{6}{7}$

Cross multiplying,

=> 7 ( 5x + 5) = 6 ( 6x + 5)

=> 35x + 35 = 36x + 30

=> 35x - 36x = 30 - 35

=> - x = - 5

=> x = 5

Substitute x = 5 in the values of the ratio,

$\bf{\underline{\large{\boxed{\sf{\purple{Smaller\:number\:=\:5x\:=5\times\:5\:=\:25}}}}}}$

$\bf{\underline{\large{\boxed{\sf{\purple{Greater\:number\:=\:6x\:=6\times\:5\:=\:30}}}}}}$