Question

Two two-digit numbers are in the ratio 6:4. When x is subtracted from antecedent and y is added to consequent,the ratio becomes 1:5 Find the values of x and y.
(a)x=10;y=50 (b)x=50;y=10 (c)x=60;y=40 (d)none​

Answer 1

Answer:

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Step-by-step explanation:

Let x and y be the numbers.

Given,x:y=4:5 or  

y

x

​

=  

5

4

​

 

x=  

5

4y

​

       …(1)

x−30:y−30=1:2 or  

y−30

x−30

​

=  

2

1

​

 

2(x−30)=y−30

x=  

2

y+30

​

 …(2)

From (1) and (2):

5

4y

​

=  

2

y+30

​

 

8y=5y+150

3y=150⟹y=50

Substituting this value of y in (1):

x=  

5

4y

​

=  

5

4(50)

​

=40

∴40 and 50 are the numbers.

Answer 2

Answer:

Required value of x is 5 and value of y is 1.

So, option d is the correct answer.

Step-by-step explanation:

Given, two two-digit numbers are in the ratio 6:4.

Again given,x is subtracted from antecedent and y is added to consequent.

6 is antecedent and 4 is consequent in the ratio 6:4.

Now antecedent is $(6 - x)$

and consequent is $(4 + y)$

It is also given now ratio is 1:5.

So, according to question,

$\frac{6 - x}{4 + y} = \frac{1}{5}$

Here 1 and 5 don't have any common factor other than 1.

So,we can say

$6 - x = 1 \\ x = 6 - 1 \\ x = 5$

and

$4 + y = 5 \\ y = 5 - 4 \\ y = 1$

Required value of x is 5 and value of y is 1.

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