Question

Two numbers are that the ration between is 4:5 but if each increased by 10 ,the ratio between them become 6:7 what is the number​

Answer 1

Given :-

ratio between two numbers is 4 : 5

let the two numbers be 4x and 5x respectively.

ATQ, if each of them is increased by 10, then the new ratio becomes 6 : 7

we've to find the numbers.

➡ (4x + 10)/(5x + 10) = 6/7

by cross multiplying we get,

➡ 7(4x + 10) = 6(5x + 10)

➡ 28x + 70 = 30x + 60

➡ 28x - 30x = 60 - 70

➡ -2x = -10

➡ x = -10/-2

➡ x = 5

hence, the numbers are :-

• 4x = 4 × 5 = 20

• 5x = 5 × 5 = 25

VERIFICATION :-

LHS :-

= (4x + 10)/(5x + 10)

= (20 + 10)/(25 + 10)

= 30/35 = 6/7

RHS :-

= 6/7

LHS = RHS. hence verified!

Answer 2

• Let one number be 4M and another number be 5M.

Each number is increased by 10

Now,

• One number = 4M + 10

• Another number = 5M + 10

» If both the numbers increased by 10 then, the ratio becomes 6 : 7.

According to question,

→ $\dfrac{4M\:+\:10}{5M\:+\:10}\:=\:\dfrac{6}{7}$

Cross-multiply them

→ 7(4M + 10) = 6(5M + 10)

→ 28M + 70 = 30M + 60

→ 28M - 30M = 60 - 70

→ - 2M = 10

→ M = 5

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One number = 4M = 4(5) = 20

Another number = 5M = 5(5) = 25

________ [ ANSWER ]

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✡ VERIFICATION :

From above calculations we have M = 5

Put value of M in this equation : $\dfrac{4M\:+\:10}{5M\:+\:10}\:=\:\dfrac{6}{7}$

=> $\dfrac{4(5)\:+\:10}{5(5)\:+\:10}\:=\:\dfrac{6}{7}$

=> $\dfrac{20\:+\:10}{25\:+\:10}\:=\:\dfrac{6}{7}$

=> $\dfrac{30}{35}\:=\:\dfrac{6}{7}$

=> $\dfrac{6}{7}\:=\:\dfrac{6}{7}$

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