Question

18
Number x is 10% more than number y Number y is 10% more than number z. How much
percent is number : less than number?​

Answer 1

★Given :

• Number x is 10% more than number y.
• Number y is 10% more than number z.

★To Find :

• Less%.

❇Solution :-

Let the number z be x.

Then, number y :

$\to{ \sf{10 \% \: more \: than \: number \: z.}}$

$\to{ \sf{x + 10\% \: of \: x}}$

$\to{ \sf{x + x \times \dfrac{1 \cancel{0}}{10 \cancel{0}} }}$

$\to{ \sf{x + \dfrac{x}{10}}}$

$\to{ \sf{\dfrac{10x + x}{10} }}$

$\to{\tt{\dfrac{11x}{10} }}$

___________________

And the number x :

$\to{\sf{ 10 \% \: more \: than \: number \: y.}}$

$\to{\sf{\dfrac{11x}{10} + 10\% \: of \: \dfrac{11x}{10} }}$

$\to{\sf{\dfrac{11x}{10} + \dfrac{11x}{ \cancel{10}} \times \dfrac{ \cancel{10}}{100} }}$

$\to{ \sf{ \dfrac{11x}{10} + \dfrac{11x}{100} }}$

$\to{ \sf{ \dfrac{110x + 11x}{100} }}$

$\to{ \tt{ \dfrac{121x}{100}}}$

___________________

$: \implies{\sf{Less = Number \: x -Number \: z }}$

$: \implies{\sf{Less = \dfrac{121x }{100} - x }}$

$: \implies{\sf{Less = \dfrac{121x - 100x}{100} }}$

$: \implies{\tt{Less = \dfrac{21x}{100} }}$

____________________

$: \implies {\sf{Less \%= \bigg( \dfrac{Less}{Number \: x} \times 100\bigg)\%}}$

$: \implies {\sf{Less \%= \bigg( \dfrac{\dfrac{21x}{100}}{\dfrac{121x}{100} } \times 100\bigg)\%}}$

$: \implies {\sf{Less \%= \bigg( \dfrac{21 \cancel{x}}{ \cancel{100}} \times \dfrac{ \cancel{100 }}{121 \cancel{x}} \times 100\bigg)\%}}$

$: \implies{ \sf{ Less \% = \bigg( \cancel{\dfrac{2100}{121}} \bigg)}}$

$: \implies{ \underline{ \boxed {\bf{\red{Less \% = 17.36 \%\: (approx) }}}}}$

$\therefore{\underline{\tt{Less\%=17.36 \%\: (approx).}}}$

Answer 2

★Given :

Number x is 10% more than number y.

Number y is 10% more than number z.

★To Find :

Less%.

❇Solution :-

Let the number z be x.

Then, number y :

$\to{ \sf{10 \% \: more \: than \: number \: z.}}$

$\to{ \sf{x + 10\% \: of \: x}}$

$\to{ \sf{x + x \times \dfrac{1 \cancel{0}}{10 \cancel{0}} }}$

$\to{ \sf{x + \dfrac{x}{10}}}$

$\to{ \sf{\dfrac{10x + x}{10} }}$

$\to{\tt{\dfrac{11x}{10} }}$

___________________

And the number x :

$\to{\sf{ 10 \% \: more \: than \: number \: y.}}$

$\to{\sf{\dfrac{11x}{10} + 10\% \: of \: \dfrac{11x}{10} }}$

$\to{\sf{\dfrac{11x}{10} + \dfrac{11x}{ \cancel{10}} \times \dfrac{ \cancel{10}}{100} }}$

$\to{ \sf{ \dfrac{11x}{10} + \dfrac{11x}{100} }}$

$\to{ \sf{ \dfrac{110x + 11x}{100} }}$

$\to{ \tt{ \dfrac{121x}{100}}}$

___________________

$: \implies{\sf{Less = Number \: x -Number \: z }}$

$: \implies{\sf{Less = \dfrac{121x }{100} - x }}$

$: \implies{\sf{Less = \dfrac{121x - 100x}{100} }}$

$: \implies{\tt{Less = \dfrac{21x}{100} }}$

____________________

$: \implies {\sf{Less \%= \bigg( \dfrac{Less}{Number \: x} \times 100\bigg)\%}}$

$: \implies {\sf{Less \%= \bigg( \dfrac{\dfrac{21x}{100}}{\dfrac{121x}{100} } \times 100\bigg)\%}}$

$: \implies {\sf{Less \%= \bigg( \dfrac{21 \cancel{x}}{ \cancel{100}} \times \dfrac{ \cancel{100 }}{121 \cancel{x}} \times 100\bigg)\%}}$

$: \implies{ \sf{ Less \% = \bigg( \cancel{\dfrac{2100}{121}} \bigg)}}$

$: \implies{ \underline{ \boxed {\bf{\red{Less \% = 17.36 \%\: (approx) }}}}}$

$\therefore{\underline{\tt{Less\%=17.36 \%\: (approx).}}}$✅