What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?

Let the number subtracted to be x.

therefore,

\[\begin{array}{*{35}{l}}

\left( 7\text{ }-\text{ }x \right):\text{ }\left( 17\text{ }-\text{ }x \right)::\text{ }\left( 17\text{ }-\text{ }x \right):\text{ }\left( 47\text{ }-\text{ }x \right)  \\

~  \\

\end{array}\]

Concise Selina Solutions Class 10 Maths Chapter 7 ex. 7(B) - 10

\[\begin{array}{*{35}{l}}

\left( 7\text{ }-\text{ }x \right)\left( 17\text{ }-\text{ }x \right)\text{ }=\text{ }{{\left( 17\text{ }-\text{ }x \right)}^{2}}  \\

329\text{ }-\text{ }47x\text{ }-\text{ }7x\text{ }+\text{ }{{x}^{2}}~=\text{ }289\text{ }-\text{ }34x\text{ }+\text{ }{{x}^{2}}  \\

329\text{ }-\text{ }289\text{ }=\text{ }-34x\text{ }+\text{ }54x  \\

20x\text{ }=\text{ }40  \\

x\text{ }=\text{ }2  \\

\end{array}\]

Therefore, the required number which must be subtracted is 2.