Question

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

Answer 1

Answer:

Z is 17.355% less than X.

X is 21% greater than Z

Step-by-step explanation:

Let us assume this from numbers,

Let's start with Z

Assume Z as 10

Now Given Y > Z by 10%

10% of Z is 1

Now the value of Y is 10+1 = 11

Next, given X > Y by 10%

10% of Y is 1.1

Now the value of X is 11+1.1 = 12.1

Now compare both X and Z those are 10 and 12.1

12.1 = 10 + 2.1

X = Z + 2.1

This shows the X is 21% greater than Z

Now, to compare X with Z

(2.1/12.1) *100 = 17.355

This shows that Z is 17.355% less than X.

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 :

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

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

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

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

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

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

___________________

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

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

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

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

____________________

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

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

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

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

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

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