Find divisor and quotient

Question

In a long division sum the remainders from first to last are 221,301,334 and 280. Find divisor and quotient if dividend is 987654?

Answer 1

Le y is divisor, y >334 ( largest given remainder)  and  abcd is quotient

so

a*y+221 =987        ---- ---- (I)   

b*y+301 =2216      -----------(II)               

c*y+334 =3015     -------------(III)

d*y+280=3344      --------------(IV)

 

from eq (I)

a*y =766        

if a= 1 then  y = 766 or if  a= 2 y= 383  (a cannot be greater than 2 bcoz y> 334)

from eq (II)

b*y =1915   

putting values of y from above if y = 766 then b= 2.5 or if y = 383 then b= 5

b cannot be 2.5   so y = 383 , b = 5 , a = 2.

from eq(III)

c= 7

from eq (IV)

d= 8

987654 / y = abcd + 280/y

y (divisor) = 383

abcd (quotient) = 2578

Remainder = 280