In a certain sum the dividend is 37693, the quotient is 52and the remainder is greater than 52 but less than 104.Find the divisor
Answers
Solution :-
given that,
→ Dividend = 37693
and,
→ Quotient = 52
so, in order to find divisor , dividing dividend by Quotient we get ,
→ 37693 ÷ 52 ≈ 724
taking 724 as divisor now,
→ Dividend = 37693
→ Divisor = 724
so,
→ Quotient = 52
→ Remainder = 45
since remainder is less than 52 .
taking 1 less than 724 divisor we get,
→ Dividend = 37693
→ Divisor = 723
so,
→ Quotient = 52
→ Remainder = 97
as we can see that, remainder is greater than 52 but less than 104.
therefore, we can conclude that, the divisor is 723 .
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Given : dividend is 37693, the quotient is 52and the remainder is greater than 52 but less than 104.
To Find : the divisor
Solution:
a=bq+r
a = dividend = 37693
b = divisor = ?
q = quotient = 52
r = remainder 52 < r < 104
0 ≤ r < b
52 < r < 104
=> 52 <52 +r' < 104
=> 0 < r' < 52
37693 = b(52) + 52 + r'
=> 37693 = (52)(b + 1) + r'
Taking 52 as Divisor , b + 1 will be Quotient as 0 < r' < 52
and b will be our required Divisor for initial condition
724
52 _| 37693 |_
364
_____
129
104
_____
253
208
_____
45
724 = b + 1
=> b = 723
Hence the divisor is 723
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