Question

solve this problem :) ​

Answer 1

Correct Question :

The ratio of two number is 8:7 .If 2 subtracted from both the number, the ratio changes to 7:6. Find the numbers.

Reason : In this Question the conditions not accept the 7:8. Other thing 7:6 is accept the condition of this Question and Correct ratio According to Books too.

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Given,

The Ratio of two number is 8:7

If 2 is subtracted from the numbers then the ratio changes to 7:6

To Find,

The Required Number

Solution :

$\implies$ Suppose the First number be x

And, Suppose the Second Number be y

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

The Ratio of two numbers is 8:7.

$\implies \sf{\dfrac{Ratio \ of \ First \ Number }{Ratio \ of \ Second \ Number} = \dfrac{8}{7}}$

$\implies \sf{\dfrac{x}{y} = \dfrac{8}{7}}$

$\implies \boxed{\sf{7x = 8y}}$   1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

If 2 is subtracted from both the numbers then the ratio changes to 7:8.

$\implies \sf{\dfrac{x - 2}{y - 2} = \dfrac{7}{6}}$

$\implies \sf{6(x - 2) = 7(y - 2)}$

$\implies \sf{6x - 12 = 7y - 14}$

$\implies \sf{6x - 7y = - 14 + 12}$

$\implies \sf{6x - 7y = -2}$

$\implies \sf{6x = -2 + 7y}$

$\implies \sf{x = \dfrac{7y - 2}{6}}$     2)Equation

Now Put the value of x in First Equation :-

$\implies \sf{7x = 8y}$

$\implies \sf{7(\dfrac{7y - 2}{6} ) = 8y}$

$\implies \sf{\dfrac{49y - 14}{6} - 8y = 0}$

$\implies \sf{\dfrac{49y - 14 - 48y}{6} = 0}$

$\implies \sf{49y - 48y - 14 = 0}$

$\implies \boxed{\sf{y = 14}}$

Now Put the Value of y in Second Equation :-

$\implies \sf{x = \dfrac{7y - 2}{6}}$

$\implies \sf{x = \dfrac{7(14) - 2}{6}}$

$\implies \sf{x = \dfrac{98 - 2}{6}}$

$\implies \sf{x = \dfrac{96}{6}}$

$\implies \boxed{\sf{x = 16}}$

Therefore,

$\boxed{\bold{\red{First \ Number = x = 16}}}$

$\boxed{\bold{\red{Second \ Number = y = 14}}}$

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Answer 2

Answer:

x=96/6

x=16

hope it helps you. Thanks.