Ramya told Krishna “12 times the date of my birth added to 31 times the month of my birth is 376”. On which date was Ramya born?
Answers
Given :- Ramya told Krishna “12 times the date of my birth added to 31 times the month of my birth is 376”. On which date was Ramya born ?
Solution :-
Let us assume that, Ramaya was born on D date in the month of M . where 1 ≤ D ≤ 31 and 1 ≤ M ≤ 12 .
so,
→ 12 * D + 31 * M = 376
→ 12D = 376 - 31M
→ D = (376 - 31M)/12
putting values of M from 1 to 12 for positive integer we get,
- M = 1 => (376 - 31)/12 = 345/12 ≠ integer .
- M = 2 => (376 - 31*2)/12 = 314/12 ≠ integer .
- M = 3 => (376 - 31*3)/12 = 283/12 ≠ integer .
- M = 4 => (376 - 31*4)/12 = 252/12 = 21 = integer .
- M = 5 => (376 - 31*5)/12 = 221/12 ≠ integer .
- M = 6 => (376 - 31*6)/12 = 190/12 ≠ integer .
- M = 7 => (376 - 31*7)/12 = 159/12 ≠ integer .
- M = 8 => (376 - 31*8)/12 = 128/12 ≠ integer .
- M = 9 => (376 - 31*9)/12 = 97/12 ≠ integer .
- M = 10 => (376 - 31*10)/12 = 66/12 ≠ integer .
- M = 11 => (376 - 31*11)/12 = 35/12 ≠ integer .
- M = 12 => (376 - 31*12)/12 = 4/12 ≠ integer .
therefore,
→ Only possible value of M = 4
then,
→ D = 21
Hence, Ramya was born on 21 April .
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Given : Ramya told Krishna “12 times the date of my birth added to 31 times the month of my birth is 376”.
To Find : On which date was Ramya born
Solution:
Date = x x is integer from 1 to 31
Month = y y is integer from 1 to 12
12x + 31y = 376
=> x = (376 - 31y) /12
=> x = 31 + ( 4 - 31y)/12
Hence 31y - 4 = 12k
=> 31y = 4(3k + 1)
so y = 4 , y = 8 and y = 12 are possible values
y = 4 => k = 10
y = 8 => k = 61/3 hence not possible
y = 12 => k = 92/3 hence not possible
12x + 31y = 376
y = 4 => x = 21
Hence 21st April
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