The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both th

Question

The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both the numerator and denominator, the value of the resulting fraction is 1/2 . The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5 . Find the original fraction

25/52

36/63

37/73

48/84

Answer 1

Just test them all and you'll see that 37/73 meets the criteria.



Subtract 1 from each and you have 36/72 = 1/2



The extra bit of information is unnecessary but:

7-3 = 4

7+3 = 10

4/10 = 2/5



Answer:

37/73



If you were to go the long way and try and solve this you would do the following.



Let a be the tens digit

Let b be the units digit

We know that a < b for the ratio to be 1/2.



10a+b-1 ... 1

------------ = --

10b+a-1 ... 2



Cross multiply:

2(10a+b-1) = 10b+a-1

20a + 2b - 2 = 10b + a - 1

19a - 8b - 1 = 0



Then use the next piece of information:

b-a ... 2

----- = ---

b+a ... 5



Cross multiply again:

5(b-a) = 2(b+a)

5b - 5a = 2b + 2a

7a - 3b = 0



You have two equations and two unknowns:

19a - 8b - 1 = 0

7a - 3b = 0



Multiply the first by 3 and the second by 8:

57a - 24b = 3

56a - 24b = 0



Subtract the second from the first:

a = 3



From there you can easily figure out b:

7a - 3b = 0

7(3) - 3b = 0

21 - 3b = 0

3b = 21

b = 21/3

b = 7



Answer:

37/73

Answer 2

The numerator and denominator of a fraction are interior the ratio 2 : 5. If the unique fraction is a/b: a/b = 2/5, 4/10, 6/15, 8/20, 10/25,....... If 2 is subtracted from the two numerator and denominator, the ensuing fraction is comparable to a million/3. (a - 2)/(b - 2) = 0/3, 2/8, 4/13, 6/18, 8/23,.... (a - 2)/(b - 2) = a million/3, 2/6, 3/9, 4/12, 5/15, 6/18, 7/21,.... consequently the unique fraction is 8/20

Answer 3

You only need the first part of this question to solve it. The resulting fraction of 1/2 by subtracting 1 from the numerator and denominator only leaves one choice.



24/51 not equal 1/2...

35/62

36/72

47/83



Think carefully and try to figure these out and you'll understand the question and the answer.

Answer 4

37/73