Que: The number of cars this year decreased by 20% compared to last year. The number of mobiles this year has increased by 30% compared to last year. If the total number of cars and mobiles this year increased by 10% compared to last year, what was the ratio of the number of cars to the number of mobiles last year?
A. 1:2
B. 3:2
C. 2:3
D. 4:5
E. 5:4
Que: The number of cars this year decreased by 20% compared to last year.
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- Max@Math Revolution
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Solution: Now let's solve this PS question using IVY Approach.
IVY Approach -> IVY Approach 3-2: 100c = Cars ; 100m= Mobiles
=> Percentage question ->100 -> c = cars ; m = mobiles
=> This year cars = 80% of 100c = 80c \(\left(20\%\ decrease\right)\)
=> This year mobiles = 130% of 100m = 130m \(\left(30\%\ increase\right)\)
=> Total Vehicles this year: 110% of(100c + 100m) = 110c + 110m \(\left(30\%\ increase\right)\)
=> 80c + 130m = 110c + 110m
=> 130m – 110m = 110c – 80c
=> 20m = 30c
=> c = \(\frac{2}{3}\)m
=> ∴ 100c : 100m =c :m= \(\frac{2}{3}\) m: m = 2 :3
Therefore, C is the correct answer.
Answer C
IVY Approach -> IVY Approach 3-2: 100c = Cars ; 100m= Mobiles
=> Percentage question ->100 -> c = cars ; m = mobiles
=> This year cars = 80% of 100c = 80c \(\left(20\%\ decrease\right)\)
=> This year mobiles = 130% of 100m = 130m \(\left(30\%\ increase\right)\)
=> Total Vehicles this year: 110% of(100c + 100m) = 110c + 110m \(\left(30\%\ increase\right)\)
=> 80c + 130m = 110c + 110m
=> 130m – 110m = 110c – 80c
=> 20m = 30c
=> c = \(\frac{2}{3}\)m
=> ∴ 100c : 100m =c :m= \(\frac{2}{3}\) m: m = 2 :3
Therefore, C is the correct answer.
Answer C
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