Question

If d is the HCF of 65 and 117, then it can be written in the form d = 65a + 117b or d = 65x + 117y. Find the possible
values of a, b, x and y.

Answer 1

Hello there !

Euclid's Division Lemma :-

a = bq +r

117 > 65

117 = 65 × 1 + 52 ----> [ 2 ]

65 = 52 x 1 + 13 -----> [1]

52 = 13 x 4 + 0

HCF = 13

13 = 65x + 117y

From [ 1] ,

13 = 65 - 52 x 1

From [2] ,

52 = 117 - 65 x 1 ----> [3]

Hence ,

13 = 65 - [ 117 - 65 x 1 ] ------> from [3]

= 65 x 2 - 117

= 65 x 2 + 117 x [-1 ]

x= 2

x= 2y =-1

Answer 2

Step-by-step explanation:

the principal amount be equal to P. Let the rate at which the interest is levied is equal to R% per annum (per year). let the time for which the amount is lent = T years. Then we can write:

Simple Interest = [{P×R×T}/100]

We can also calculate the Principal amount as P = [{100×(Simple Interest)}/(R×T)].

Similarly, we can write the time T as equal to T