1. A two digit number becomes five-sixth of itself
when its digits are reversed. The two digits differ
by 1. The number is
2.The ratio of the present ages of two brothers is
1: 2 and 5 years back the ratio was 1: 3. What
will be the ratio of their ages after 5 year
Answers
» Question (1).
A two digit number becomes five-sixth of itself
when its digits are reversed. The two digits differ
by 1. Then Find the two-digit number.
» Solution :
→ Taken :
Let the digits of the two-digit number be x and y.
- Original number = (10a + b)
- No. obtained on reversing the digits = 10(b + a)
→ Concept :
According to the question , it says that the Original number became ⅚th of itself when the digits are interchanged.
So the equation formed is :
→ Given :
- Difference of the digits of the number is 1.i.e,
(Equation.2)
To Find the Equation 1 :
Given Equation :
By solving it , we get :
Taking the common 11, we get :
[Anything divided by 0 is 0]
(Equation.1)
→ Calculation :
Putting the Two Equations .i.e,(i) and (ii), we get :
__________________
__________________[By Subtracting]
Hence ,the value of a is 5.
Putting the value of a in Equation 1 , we get :
Hence ,the value of b is 4.
The original number :
- a = 5
- b = 4
Putting the value of a and b in the Equation , (10a + b) , we Get :
So, the two-digit number is 54.
» Question (2) :
The ratio of the present ages of two brothers is
1: 2 and 5 years back the ratio was 1: 3. What
will be the ratio of their ages after 5 years .
» Solution :
→ We Know :
Let the present ages of the two brothers be x and 2x.
Ratio before 5 years is 1 : 3.
So the ages of the two brothers before 5 years with respect to present age will be (x - 5) and (2x - 5)
→ Concept :
According to the question , The Ratio of ages of two brothers before 5 years will be Equal to Ratio before 5 years with respect to the present ages of two brothers.
So the equation formed is :
By solving this Equation , we will get the Present age of two brothers.
→ Calculation :
Given Equation :
By solving cross multiplication , we get :
Hence ,the present age of one brother is 10 and the present age of another brother is 2x. So his present age is 20 years.
Ratio of Age after 5 years.
- Age of first brother after 5 years =
➝ Present age + 5 years
➝ 10 + 5 = 15 years.
- Age of second brother after 5 years =
➝ Present age + 5 years
➝ 20 + 5 = 25 years
Ratio :
Age of first brother after 5 years : Age of second brother after 5 years.
Hence , the ratio of their ages after 5 years is 3 : 5.
» Additional information :
- Profit Percentage =
- Loss Percentage =
- Selling Price =
_________________________
A.T.Q
now,
_________________________
2) 35:25 or 7:5
EXPLANATION:-
(see in attachment)
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![](https://hi-static.z-dn.net/files/dba/09fb98834401ba7b64581b13be061466.jpg)
![](https://hi-static.z-dn.net/files/d6e/41365afdae7bfe668047353e465b005a.jpg)