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03 Nov 2014, 09:47
Kudos
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C
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Difficulty:
45%
(medium)
Question Stats:
72% (02:44) correct
28%
(03:09)
wrong
based on 802
sessions
History
Date
Time
Result
Not Attempted Yet
x years ago, Cory was one fifth as old as Tania. In x years, Tania will be twice as old as Cory. What is the ratio of Cory's current age to Tania's current age?
(A) 7:23
(B) 9:17
(C) 5:13
(D) 3:7
(E) 11:15
(A) 7:23
(B) 9:17
(C) 5:13
(D) 3:7
(E) 11:15
03 Nov 2014, 23:02
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Let current age of Cory = c & Tania = a
Setting up the equations:
\(\frac{c-x}{t-x} = \frac{1}{5}\) ............. (1)
\(\frac{c+x}{t+x} = \frac{1}{2}\) ........... (2)
Simplify (1)
5c - t = 4x ................... (3)
Simplify (2)
2c - t = -x ................... (4)
(3)/(4)
13c = 5t
\(\frac{c}{t} = \frac{5}{13}\)
Answer = C
Setting up the equations:
\(\frac{c-x}{t-x} = \frac{1}{5}\) ............. (1)
\(\frac{c+x}{t+x} = \frac{1}{2}\) ........... (2)
Simplify (1)
5c - t = 4x ................... (3)
Simplify (2)
2c - t = -x ................... (4)
(3)/(4)
13c = 5t
\(\frac{c}{t} = \frac{5}{13}\)
Answer = C
03 Nov 2014, 14:06
Kudos
Bookmarks
C is Cory's current age, & T is Tania's current age.
First Eqn:
c-x = (1/5)(T-x)
Second Eqn:
T+x=2(c+x)
Find x in terms of C & T from the 1st Eqn, x=(5/4)c-(1/4)T, plug this value of x in the 2nd Eqn
T+x=2c+2x, T-2c=x, T-2c=(5/4)c-(1/4)T, Bring T on one side of the Eqn and C on the other, (5/4)T=(13/4)c, thus C/T = 5/13
First Eqn:
c-x = (1/5)(T-x)
Second Eqn:
T+x=2(c+x)
Find x in terms of C & T from the 1st Eqn, x=(5/4)c-(1/4)T, plug this value of x in the 2nd Eqn
T+x=2c+2x, T-2c=x, T-2c=(5/4)c-(1/4)T, Bring T on one side of the Eqn and C on the other, (5/4)T=(13/4)c, thus C/T = 5/13
