**Question 1. Without performing actual addition and division write the quotient when the sum of 69 and 96 is divided by**

**(i) 11 (ii) 15**

**Solution:**

**(i) 11**

According to the rule when ab + ba is divided by 11 then the quotient is (a + b) if a and b are digits of the numbers.

Therefore, the sum of 69 and 96 is when divided by 11 then we will get

a + b = 6 + 9 = 15

Hence, our quotient is 15.

**(ii) 15**

According to the rule when ab + ba is divided by (a + b) then the quotient is 11 if a and b are digits of the numbers.

Therefore, the sum of 69 and 96 is when divided by 15 then we will get 11 as quotient.

Hence, our quotient is 15.

**Question 2. Without performing actual computations, find the quotient when 94-49 is divided by**

**(i) 9 (ii) 5**

**Solution:**

**(i) 9**

According to the rule when ab – ba is divided by 9 then the quotient is (a – b) if a and b are digits of the numbers and are having reverse digits.

Therefore, the computation of 94 -49 is when divided by 9 then we will get

a – b = 9 – 4 = 5

Hence, our quotient is 5.

**(ii) 5**

According to the rule when ab – ba is divided by (a – b) then the quotient is 9 if a and b are digits of the numbers and are having reverse digits.

Therefore, the computation of 94 -49 is when divided by 5 then we will get 9 as our quotient.

**Question 3. If sum of the number 985 and two other numbers obtained by arranging the digits of 985 in cyclic order is divided by 111, 22 and 37 respectively. Find the quotient in each case.**

**Solution:**

When the sum of a 3 digit cyclic number is divided by 111 then the quotient is the value of the sum of its digits.

i.e.

9 + 8 + 5 = 22.

Hence our quotient is 22.

According to the rule, the sum of a 3 digit cyclic number is when divided by the sum of its digits, then the quotient obtained is 111.

When, 3 × 37 = 111

Quotient = 3 × (Sum of the digits) = 3 × 22 = 66

**Question 4. Find the quotient when the difference of 985 and 958 is divided by 9.**

**Solution:**

According to the rule, when unit’s and ten’s digits are interchanged, then the difference of the numbers when divided by 9, gives a quotient as the difference between the unit’s and the ten’s digit.

Quotient is 8 – 5 = 3