Question and Answers Forum

All Questions      Topic List

Logic Questions

Previous in All Question      Next in All Question      

Previous in Logic      Next in Logic      

Question Number 118825 by bramlexs22 last updated on 20/Oct/20

I am thinking of a two−digit number  .If i write 3 to the left of my number  and double this three digit number the  result is 27 times my original number.  what is my number ?

$${I}\:{am}\:{thinking}\:{of}\:{a}\:{two}−{digit}\:{number} \\ $$$$.{If}\:{i}\:{write}\:\mathrm{3}\:{to}\:{the}\:{left}\:{of}\:{my}\:{number} \\ $$$${and}\:{double}\:{this}\:{three}\:{digit}\:{number}\:{the} \\ $$$${result}\:{is}\:\mathrm{27}\:{times}\:{my}\:{original}\:{number}. \\ $$$${what}\:{is}\:{my}\:{number}\:? \\ $$

Answered by benjo_mathlover last updated on 20/Oct/20

let original your number is AB   then 2×3AB = 27×AB  ⇒2(300+10A+B)=27(10A+B)  ⇒600+20A+2B=270A+27B  ⇒600=250A+25B   ⇒24 = 10A+B . Thus your number is 24

$${let}\:{original}\:{your}\:{number}\:{is}\:{AB}\: \\ $$$${then}\:\mathrm{2}×\mathrm{3}{AB}\:=\:\mathrm{27}×{AB} \\ $$$$\Rightarrow\mathrm{2}\left(\mathrm{300}+\mathrm{10}{A}+{B}\right)=\mathrm{27}\left(\mathrm{10}{A}+{B}\right) \\ $$$$\Rightarrow\mathrm{600}+\mathrm{20}{A}+\mathrm{2}{B}=\mathrm{270}{A}+\mathrm{27}{B} \\ $$$$\Rightarrow\mathrm{600}=\mathrm{250}{A}+\mathrm{25}{B}\: \\ $$$$\Rightarrow\mathrm{24}\:=\:\mathrm{10}{A}+{B}\:.\:{Thus}\:{your}\:{number}\:{is}\:\mathrm{24} \\ $$

Answered by MJS_new last updated on 20/Oct/20

2×(300+x)=27x  600=25x  x=24

$$\mathrm{2}×\left(\mathrm{300}+{x}\right)=\mathrm{27}{x} \\ $$$$\mathrm{600}=\mathrm{25}{x} \\ $$$${x}=\mathrm{24} \\ $$

Commented by PRITHWISH SEN 2 last updated on 20/Oct/20

simple and beautiful

$$\mathrm{simple}\:\mathrm{and}\:\mathrm{beautiful} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com