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# Misha is 10 years older than Tanya. However 5 years ago, Misha was twi

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Math Expert
Joined: 02 Sep 2009
Posts: 64095
Misha is 10 years older than Tanya. However 5 years ago, Misha was twi  [#permalink]

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31 Jul 2019, 08:27
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Difficulty:

25% (medium)

Question Stats:

74% (01:16) correct 26% (00:59) wrong based on 43 sessions

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Misha is 10 years older than Tanya. However 5 years ago, Misha was twice as old as Tanya. How old is Tanya ?

A. 5
B. 10.
C. 12
D. 13
E. 15

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Math Expert
Joined: 02 Sep 2009
Posts: 64095
Re: Misha is 10 years older than Tanya. However 5 years ago, Misha was twi  [#permalink]

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31 Jul 2019, 08:28
Bunuel wrote:
Misha is 10 years older than Tanya. However 5 years ago, Misha was twice as old as Tanya. How old is Tanya ?

A. 5
B. 10.
C. 12
D. 13
E. 15

Check other Age Problems in our Special Questions Directory.
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Joined: 18 May 2019
Posts: 811
Misha is 10 years older than Tanya. However 5 years ago, Misha was twi  [#permalink]

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31 Jul 2019, 08:35
1
Ma=Ta+10.....(1)
Five years ago, Ma-5=2(Ta-5)
Ma=2Ta-5....(2)
Put (2) into (1)
2Ta-5=Ta+10
Hence Ta=15

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Re: Misha is 10 years older than Tanya. However 5 years ago, Misha was twi  [#permalink]

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31 Jul 2019, 09:18
Bunuel wrote:
Misha is 10 years older than Tanya. However 5 years ago, Misha was twice as old as Tanya. How old is Tanya ?

A. 5
B. 10.
C. 12
D. 13
E. 15

m=t+10
m-5=2t-10
t+5=2t-10
t=15
IMO E
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Re: Misha is 10 years older than Tanya. However 5 years ago, Misha was twi  [#permalink]

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05 Aug 2019, 16:14
Bunuel wrote:
Misha is 10 years older than Tanya. However 5 years ago, Misha was twice as old as Tanya. How old is Tanya ?

A. 5
B. 10.
C. 12
D. 13
E. 15

We can let M = Misha’s current age and T = Tanya’s current age and create the equation:

M = 10 + T

Five years ago, Misha was (M - 5) years old, and Tanya was (T - 5) years old. Thus, we can express the relationship between their ages then as:

M - 5 = 2(T - 5)

M - 5 = 2T - 10

M = 2T - 5

Since both equations are equal to M, we can set them equal to each other:

10 + T = 2T - 5

15 = T

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Re: Misha is 10 years older than Tanya. However 5 years ago, Misha was twi   [#permalink] 05 Aug 2019, 16:14