# If twice the numerator is 2 more than the denominator and if 3 is added to each, new fraction is 2/3. Find the number?

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In a rational number,
twice the numerator is 2 more than the denominator.
If 3 is added to each i.e. the numerator and the denominator, the new fraction is 2/3.

Find the original number?

posted Dec 28, 2016

let the numerator be a and the denominator b. One of the equations is 2a=b+2. The other equation is (a+3)/b+3)=2/3. The solution gives a=7 and b=12. First check 2*7=12+2. Second check (7+3)/(12+3)=2/3

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+1 vote

3 rational numbers form a geometric progression in its current order.

1. If 8 is added to the middle number, then this new sequence forms an arithmetic progression.
2. If 64 is later added to the last number, then this yet another sequence forms a geometric progression again.
3. First number of these sequences is an integer.

Find the numbers?