Question

two no are in the ratio 3:5. If each no. is increased by 10, the ratio becomes 5:7. The sum of the no.is​

Answer 1

Answer :-

The sum of the numbers is 40 respectively.

Explanation :-

Given :

• Ratio of two numbers - 3 : 5
• Ratio of the numbers when increased by 10 - 5 : 7

To find :

The sum of the numbers which are in the ratio 3 : 5

Solution :

Let the first number be 3x

and the second be 5x

When increased by 10,

The first number = (3x + 10)

The second number = (5x + 10)

According to question,

$= > \dfrac{3x + 10}{5x + 10} = \dfrac{5}{7}$

By cross multiplying the terms,

$= > 5(5x + 10) = 7(3x + 10)$

$= > 25x + 50 = 21x + 70$

$= > 25x - 21x = 70 - 50$

$= > 4x = 20$

$= > x = \dfrac{20}{4}$

$= > x = 5$

Hence the value of x is 5.

Therefore,

The first number => 3 × 5 = 15

The second number => 5 × 5 = 25

Now,

The sum of the numbers :-

= First number + Second number

= 15 + 25

= 40

Hence, the sum of the numbers is 40.

Answer 2

Question:

Two numbers are in the ratio 3:5. If each no. is increased by 10, the ratio becomes 5:7. The sum of the number is?

Solution:

• Let first number be 3M and other number be 5M.

Both numbers are increased by 10

Now..

• First number = 3M + 10

• Other number = 5M + 10

And the ratio of both the numbers is 5 :7

A.T.Q.

=> $\dfrac{3M\:+\:10}{5M\:+\:10}$ = $\dfrac{5}{7}$

Cross-multiply them

=> 7(3M + 10) = 5(5M + 10)

=> 21M + 70 = 25M + 50

=> 21M - 25M = 50 - 70

=> - 4M = - 20

=> M = 20/4

=> M = 5

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• First number = 3M = 3(5) = 15

• Other number = 5M = 5(5) = 25

Sum of the numbers = First number + Other number

=> 15 + 25

=> 40

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The sum of the numbers is 40

__________ [ ANSWER ]

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✡ Verification :

From above calculations we have M = 5

Put value of M in this equation :

$\dfrac{3M\:+\:10}{5M\:+\:10}$ = $\dfrac{5}{7}$

=> $\dfrac{3(5)\:+\:10}{5(5)\:+\:10}$ = $\dfrac{5}{7}$

=> $\dfrac{15\:+\:10}{25\:+\:10}$ = $\dfrac{5}{7}$

=> $\dfrac{25}{35}$ = $\dfrac{5}{7}$

=> $\dfrac{5}{7}$ = $\dfrac{5}{7}$

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