Question

A number when divided by 259 leaves a remainder 139. What will be the remainder when the same number is divided by 37?
(A) 28 (B) 29
(C) 30 (D) 31

Answer 1

Step-by-step explanation:

28

Let the dividend be n. Let the quotient be q. Thus the remainder is 28. Hence the number when the same number divided by 37 is 28.

Answer 2

Answer:

(A) 28 is the answer for the given question

Step-by-step explanation:

Given :

A number when divided by 259 leaves a remainder 139

To find :

remainder when the same number is divided by 37. Options are :

(A) 28

(B) 29

(C) 30

(D) 31

Solution :

Let the number divided by 259 and leaving a remainder 139 be n. Let the quotient for this condition be x

So, according to Euclid's Division Lemma, we know that

$\boxed{\mathrm{Dividend = Divisor \times Quotient + Remainder}}$

Here, n = Dividend

259 = divisor

x = quotient

139 = remainder

Thus, it can be written as

n = 259x + 139

Now, question is that if we divide 37 with n, what will be the remainder

So, dividing n with 37

$\implies \mathrm{\dfrac{n}{37} = \dfrac{259x}{37} + \dfrac{139}{37}}$

$\implies \mathrm{\dfrac{n}{37} = 7x + \dfrac{139}{37}}$

$\implies \mathrm{\dfrac{n}{37} =7x + 3 + \dfrac{28}{37}} \ \ ---- \bigg[\dfrac{139}{37} = 3 + \dfrac{28}{37}\bigg]$

Let 7x + 3 = m [This is the quotient when divided by 37]

$\implies \mathrm{\dfrac{n}{37} = m + \dfrac{28}{37}}$

$\implies \mathrm{n = 37m + 28}$

This is of the form of Euclid's Division Lemma,

where, n = dividend ; 37 = divisor ; m = quotient ; 28 = remainder

$\underline{\boxed{\textsf{Thus, remainder is {\Large{28}} when the number is divided by 37}}}$

Hope it helps!!