Class 6 Operations on whole Numbers Exercise 4.4-2

\begin{array}{l} \text {Q4. Divide and check the quotient and remainder: } \\ (i) \quad 7772 \div 58 \\ (ii) \quad 6906 \div 35 \\ (iii) \quad 16135 \div 875 \\ (iv) \quad 16025 \div 1000 \\ \\\text {Sol. } (i) \quad 7772 \div 58 \\ \end{array}\begin{array}{r|rc} & 134 & \leftarrow Q\\ \hline 58 & 7772 & \\ & -58 &\\ \hline & 197 & \\ & -174 &\\ \hline & 232 & \\ & -232 &\\ \hline & 0 & \leftarrow R \\ \hline \end{array}\begin{array}{l} \therefore \text {Dividend} = 7772 \\ \text {Divisor} = 58 \\ \text {Quotient} = 134 \\ \text {Remainder} = 0 \\\text {Verification : Divisor x Quotient + Remainder} \\ =58 \times 134 + 0 = 7772 = \text {Dividend}\\ \text {Hence checked.} \\ \\(ii) \quad 6906 \div 35 \\ \end{array}\begin{array}{r|rc} & 197 & \leftarrow Q\\ \hline 35 & 6906 & \\ & -35 &\\ \hline & 340 & \\ & -315 &\\ \hline & 256 & \\ & -245 &\\ \hline & 11 & \leftarrow R \\ \hline \end{array}\begin{array}{l} \therefore \text {Dividend} = 6906 \\ \text {Divisor} = 35 \\ \text {Quotient} = 197 \\ \text {Remainder} = 11 \\\text {Verification : Divisor x Quotient + Remainder} \\ =35 \times 197 + 11 = 6906 = \text {Dividend}\\ \text {Hence checked.} \\ \\(iii) \quad 16135 \div 875 \\ \end{array}\begin{array}{r|rc} & 18 & \leftarrow Q\\ \hline 875 & 16135 & \\ & -875 &\\ \hline & 7385 & \\ & -7000 &\\ \hline & 385 & \leftarrow R \\ \hline \end{array}\begin{array}{l} \therefore \text {Dividend} = 16135 \\ \text {Divisor} = 875 \\ \text {Quotient} = 18 \\ \text {Remainder} = 385 \\\text {Verification : Divisor x Quotient + Remainder} \\ =875 \times 18 + 385 = 16135 = \text {Dividend}\\ \text {Hence checked.} \\ \\(iv) \quad 16025 \div 1000 \\ \end{array}\begin{array}{r|rc} & 16 & \leftarrow Q\\ \hline 1000 & 16025 & \\ & -1000 &\\ \hline & 6025 & \\ & -6000 &\\ \hline & 25 & \leftarrow R \\ \hline \end{array}\begin{array}{l} \therefore \text {Dividend} = 16025 \\ \text {Divisor} = 1000 \\ \text {Quotient} = 16 \\ \text {Remainder} = 25 \\\text {Verification : Divisor x Quotient + Remainder} \\ =1000 \times 16 + 25 = 16025 = \text {Dividend}\\ \text {Hence checked.} \\ \\\text {Q5. Find a number which when divided by 35 gives the quotient 20 and remainder 18. } \\\text {Sol. We know that Dividend = Divisor x Quotient + Remainder } \\ \text {By substituting the given values, we get } \\ \text {Dividend} =35 \times 20 + 18 =700+18 =718 \\ \\\text {Q6. Find the number which when divided by 58 gives a quotient 40 and remainder 31.} \\ \\\text {Sol. We know that Dividend = Divisor x Quotient + Remainder } \\ \text {By substituting the given values, we get } \\ \text {Dividend} =58 \times 40+31 \\ =2320+31 =2351 \\ \\\text {Q7. The product of two numbers is 504347. If one of the numbers is 1591, find the other. } \\ \\\text {Sol. Given that the product of two numbers }=504347 \\ \text {Also, one of the number }=1591 \\ \text {Lets assume x be the another number.} \\ \Rightarrow \quad x \times 1591=504347 \\ \Rightarrow \quad x ={\large \frac {504347}{1591} } = 317 \\ \text {Hence, the other number is 317.} \\ \\\text {Q8. On dividing 59761 by a certain number, the quotient is 189 } \\ \text {and the remainder is 37. Find the divisor.} \\ \\\text {Sol. Given that Dividend } =59761 \\ \text {Quotient }=189 \\ \text {Remainder }=37 \\ \text {We know that Dividend = Divisor x Quotient + Remainder } \\ \text {By substituting the given values, we get } \\ 59761 = \text {Divisor} \times 189 + 37 \\ \Rightarrow \quad \text {Divisor} \times 189 = 59761 – 37 \\ \Rightarrow \quad \text {Divisor} = {\large \frac {59761 – 37}{189}} =316 \\ \\\text {Q9. On dividing 55390 by 299, the remainder is 75. Find the quotient. } \\ \\\text {Sol. Given that Dividend } =55390 \\ \text {Quotient }=299 \\ \text {Remainder } =75 \\\text {We know that Dividend = Divisor x Quotient + Remainder } \\ \text {By substituting the given values, we get } \\ 55390 = \text {Divisor} \times 299+75 \\\Rightarrow \quad \text {Divisor} \times 299 = 55390 – 75 \\ \Rightarrow \quad \text {Divisor} = {\large \frac {55390 – 75}{299}} =185 \\ \\\end{array}