Question

Question 6. A positive integer a is written as a = 3q + r and a = 4k + r, where q, k and r are
whole numbers.
Choose the correct possibilities of q and k?
(a) q = 4; k = 6
(b) q= 3; k= 4
(c) q = 6; k= 8
(d) q= 8; k= 6​

Answer 1

$\underline{\textbf{Given:}}$  

$\textsf{A positive integer a is written as }$

$\mathsf{a=3q+r\;\;\&\;\;a=4k+r\;\;where\;q,k\;and\;r\;are\;whole\;numbers}$  

$\underline{\textbf{To find:}}$  

$\textsf{q and k}$  

$\underline{\textbf{Solution:}}$  

$\mathsf{Consider,}$  

$\mathsf{a=3q+r\;\;\&\;\;a=4k+r}$  

$\implies\mathsf{3q+r=4k+r}$  

$\implies\mathsf{3q=4k}$  

$\implies\mathsf{\dfrac{q}{k}=\dfrac{4}{3}}$  

$\implies\mathsf{q=4m\;\;\&\;\;k=3m}$  

$\mathsf{where\;m=1,2,3\;.\;.\;.}$  

$\mathsf{For\;m=2,}$  

$\mathsf{q=8\;\;\&\;\;k=6}$  

$\therefore\mathsf{Correct\;option\;is\;(d)}$  

$\underline{\textbf{Find more:}}$

What is the answer of 64:N=8:9

https://brainly.in/question/36730035  

Answer 2

Step-by-step explanation:

(d) q= 8; k= 6

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