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07 Jul 2019, 23:27
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Difficulty:
55%
(hard)
Question Stats:
69% (03:02) correct
31%
(02:35)
wrong
based on 55
sessions
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In town A, the price of tea is defined by the expression $(100 + 0.10n) on the nth day of 2019, where n = 1, 2, ..., 100 and then remains constant. On the other hand, the price of coffee is defined by the expression $(89 + 0.15n) on the nth day of 2019, where n = 1, 2, ..., 365. On which day of the year prices of tea and coffee will be equal in town A?
A. May 21
B. April 11
C. May 20
D. April 10
E. June 30
A. May 21
B. April 11
C. May 20
D. April 10
E. June 30
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08 Jul 2019, 10:40
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T = (100+0.1n)
C = (89+0.15n)
T = (10000+10n)/100
C = (8900+15n)/100
let's try n at 100
T = 11000/100 = 110 (Max value of Tea)
C = 10400/100 = 104
Let's try n at 120
C = 10700/100 = 107
For every 20 days increase, C price increases by 3$
Then at n = 140
C = 11000/100 = 110
As the given year is not a leap year (n = 365)
Jan = 31
Feb = 28
Mar = 31
Apr = 30
May = 31
J+F+M+A+M = 151
-10 days in May as we need 140 days, i.e, May 20th
C is the answer.
C = (89+0.15n)
T = (10000+10n)/100
C = (8900+15n)/100
let's try n at 100
T = 11000/100 = 110 (Max value of Tea)
C = 10400/100 = 104
Let's try n at 120
C = 10700/100 = 107
For every 20 days increase, C price increases by 3$
Then at n = 140
C = 11000/100 = 110
As the given year is not a leap year (n = 365)
Jan = 31
Feb = 28
Mar = 31
Apr = 30
May = 31
J+F+M+A+M = 151
-10 days in May as we need 140 days, i.e, May 20th
C is the answer.
Price of Tea(T)=100+0.1*n=100+(n/10)
Price of Coffee(C)=89+0.15*n=89+(3n/20)
On the 100th day,T=110 and C=104 which means that a few more days more have to pass before C can catch up with T (which remains frozen at 110 from the 100th day onward). So we will have to figure out for which value of 'n' C will equal 110:
89+(3n/20)=110....> n=140
Calculating forward from Jan 1, that works out to May 20. ANS:C
Price of Coffee(C)=89+0.15*n=89+(3n/20)
On the 100th day,T=110 and C=104 which means that a few more days more have to pass before C can catch up with T (which remains frozen at 110 from the 100th day onward). So we will have to figure out for which value of 'n' C will equal 110:
89+(3n/20)=110....> n=140
Calculating forward from Jan 1, that works out to May 20. ANS:C
