Question

Rahul was not attentive in his class, so to give him a constructive task his teacher asked him to find two digit numbers that leaves the remainder 1 when divided by 5. Find the numbers.


Answer :-

The Ap is 11,16,21,....96.
a= 11 ,
d= 5 and
tn = 96.

We know that,
tn = a + (n-1) d
96 = 11 + (n-1) 5
96-11 = (n-1)5
85 = (n-1)5
85/5 = (n-1)
17 = n-1
17+1 = n

therefore, n=18


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Answer 1

The two digit numbers that leaves the remainder 1 when divided by 5 are 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91 and 96.

Step-by-step explanation:

The numbers which leave remainder 1 when divided by 5 are of the form d = 5n + 1. Let us check for different values of 'n' to obtain two digit numbers.

• When n = 1, d = 5 × 1 + 1 = 6, a one digit number
• When n = 2, d = 5 × 2 + 1 = 11, a two digit number
• When n = 3, d = 5 × 3 + 1 = 16, a two digit number
• When n = 4, d = 5 × 4 + 1 = 21, a two digit number
• When n = 5, d = 5 × 5 + 1 = 26, a two digit number
• ... ... ...
• When n = 18, d = 5 × 18 + 1 = 91, a two digit number
• When n = 19, d = 5 × 19 + 1 = 96, a two digit number
• When n = 20, d = 5 × 20 + 1 = 101, a three digit number

Clearly the required two digit numbers are 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91 and 96.