Question

When a number is divided by 13 remainder is 11. Same number divided by 17 leaves a remainder of 15. Find the number?

Answer 1

Answer:

x=219

Step-by-step explanation:

let the number be x

$given \\ \\x = 13a + 11 \\ also \\ x = 17b + 15 \\ so \: we \: can \: write \\ 13a + 11 = 17b + 15 \\ 13a - 17b = 4$

at this point we have one equation and two variables and can be solved only using substitution/trial and error

if we go through multiplication table of 13 and 17 we find that

$13 \times 16 = 208 \\ 17 \times 12 = 204 \\ hence \: a = 16 \: an \: b = 12$

so

$x = 13a + 11 = 208 + 11 = 219$