a) 4/7 and 5/6

b) 7/4 and 6/5

c) 4/7 and 6/5

d) 7/4 and 5/6

correct answer is : a) \frac{4}{7} and \frac{5}{6}

Explanation

Let, one number is =\ x
And, another number is =\ y
Here,
\rightarrow x\times\ y\ =\frac{10}{21}
\rightarrow x\ =\frac{10}{21}\ \div\ y
\therefore x\ =\frac{10}{21y} _{—-> (i)}
And,
\rightarrow\ \frac{x}{y}\ =\ \frac{24}{35}\
\rightarrow\ 35x\ =\ 24y
\therefore\ x\ =\ \frac{24y}{35} _{—-> (ii)}

So,
\rightarrow\ \frac{10}{21y}\ =\ \frac{24y}{35} _{[from equation (i) and (ii)]}
\rightarrow24y\ \times\ 21y\ =\ 35\ \times\ 10
\rightarrow\ 504y ² =\ 350
\rightarrow\ y ² =\ \frac{350}{504}
\rightarrow\ y ² =\ \frac{25}{36} _{[ fraction simplest form]}
\rightarrow\ y\ =\sqrt{\frac{25}{36}}
\rightarrow\ y\ =\frac{5\ \times\ 5}{6\ \times\ 6}
\rightarrow\ y\ =\frac{5}{6}

So that,
\rightarrow\ x\ \times\ y\ =\ \frac{10}{21}
\rightarrow\ x\ \times\ \frac{5}{6}\ =\ \frac{10}{21}
\rightarrow\ x\ =\ \frac{10}{21}\ \div\ \frac{5}{6}
\rightarrow\ x\ =\ \frac{10}{21}\ \times\ \frac{6}{5}
\rightarrow x\ =\ \frac{4}{7}
Ans: One number is \frac{4}{7} and another number is \frac{5}{6} .