RD Sharma solution class 8 chapter 5 Playing with numbers Exercise 5.1

Exercise 5.1

Page-5.5

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

Answer 1:

(i) Clearly, 69 and 96 are two numbers such that one can be obtained be reversing the digits of the other. Therefore, when the sum of 69 and 96 is divided by 11, we get 15 (sum of the digits) as quotient.

(ii) Clearly, 69 and 96 are two numbers such that one can be obtained be reversing the digits of the other. Therefore, when the sum of 69 and 96 is divided by 15 (sum of the digits), we obtain 11 as quotient.

Question 2:

Without performing actual computations, find the quotient when 94 − 49 is divided by
(i) 9
(ii) 5

Answer 2:

$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{when} \overline{\mathrm{ab}}-\overline{\mathrm{ba}} \mathrm{is} \mathrm{divided} \mathrm{by} 9, \mathrm{the} \mathrm{quotient} \mathrm{is} \mathrm{a}-\mathrm{b}. \\ \mathrm{Therefore}, \mathrm{when} (94-49) \mathrm{is} \mathrm{divided} \mathrm{by} 9, \mathrm{the} \mathrm{quotient} \mathrm{is} (9-4 = 5). \\ \left(\mathrm{ii}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{when} \overline{\overline{\mathrm{ab}}}-\overline{\mathrm{ba}} \mathrm{is} \mathrm{divided} \mathrm{by} (\mathrm{a}-\mathrm{b}), \mathrm{the} \mathrm{quotient} \mathrm{is} 9. \\ \mathrm{Therefore}, \mathrm{when} (94-49) \mathrm{is} \mathrm{divided} \mathrm{by} (9-4=5), \mathrm{the} \mathrm{quotient} \mathrm{is} 9. \end{gathered}$$

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.

Answer 3:

$$\begin{gathered} \mathrm{The} \mathrm{sum} \mathrm{of} (985+859+598) \mathrm{when} \mathrm{divided} \mathrm{by}: \\ \left(\mathrm{i}\right) 111 \\ Q\mathrm{uotient} = (9+8+5)=22 \\ \left(\mathrm{ii}\right) 22, \mathrm{i}.\mathrm{e}, (9+8+5) \\ Q\mathrm{uotient} = 111 \\ \left(\mathrm{iii}\right) 37 (= \frac{111}{3}) \\ Q\mathrm{uotient} = 3(9+8+5)=66 \end{gathered}$$

Question 4:

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

Answer 4:

$$\begin{gathered} \mathrm{If}\overline{ \mathrm{abc}}-\overline{\mathrm{acb}} \mathrm{is} \mathrm{divided} \mathrm{by} 9, \mathrm{the} \mathrm{quotient} \mathrm{is} (\mathrm{b}-\mathrm{c}). \\ \therefore \mathrm{If} (985-958) \mathrm{is} \mathrm{divided} \mathrm{by} 9, \mathrm{quotient}=(8-5)=3 \end{gathered}$$