Question

Find the greatest number of 5-digits which on being divided by 9, 12, 24 and 45 leaves 3, 6, 18
and 39 as remainders respectively.
​

Answer 1

$\star \; {\underline{\underline{\frak \pink{To\;find:-}}}}$

• the greatest number of 5-digits which on being divided by 9, 12, 24 and 45 leaves 3, 6, 18 and 39 as remainders respectively.

$\star \; {\underline{\underline{\frak \pink{Solution:-}}}}$

☯ The difference between the divisor and the remainder is\;same in all the cases which is 6.

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \normalsize {\underline{\underline{\sf{\blue{\dag \; Step<strong> </strong>\; (1)}}}}}$

☯ $\sf{LCM\;of\;divisors:-}$

LCM of (9,12,24,45) is 360.

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \normalsize {\underline{\underline{\sf{\blue{\dag \; Step \; (1)}}}}}$

☯ $\sf{We\;know\;the\;largest\;five\;digit\;number\;is\;99999.}$

$: \implies$ Now to find the largest five digit number which satisfy the given condition then do the following:-

$\star \; {\underline{\sf{\green{A) 360 × N - 6}}}}$

$: \implies$ N ,is the quotient of $\dfrac{99999}{360}$

$: \implies$ We shall get the answer as 360 × 277 - 6 = 97214

$\star \; {\underline{\sf{\green{ (B)\;Divide\; \dfrac{99999}{360}}}}}$

$: \implies$ We will get remainder as 279.

$: \implies \sf{ \underbrace{Subtracting\;279\;from\;99999\;which\;is\;99720.}_{ \purple{99999 - 279 = 99720}}}$

$: \implies \sf{ \underbrace{Now,\;Subtracting\;6\;from\;99720\;which\;is\;97214.}_{ \purple{99720 - 6 = 97214}}}$

$\rule{200}{2}$