Question

in a division problem product of quotient and remainder is 24 while there sum is 10 if divisor is 5 thenthen divident is​

Answer 1

the only variables whose sum is 10 and product can be 20 are 6 and 4 so 6 will be the divident and 4 will be the reminder as we know that the remainder can't be greater than the divident now when we put this into the formula divident = divisor *quotient + reminder

We will get the ans 34

Answer 2

Answer:

Dividend = 34, 26

Concept:

The relationship between divisor, dividend, remainder and quotient is as follows,

Dividend = Divisor × Quotient + Remainder            ------------------ (i)

Given:

Product of quotient and remainder, P = 24

Sum of quotient and remainder, S = 10

Divisor = 5

Find:

The value of the dividend

Solution:

Let the quotient be q and the remainder be r.

According to the question, we have

Product of quotient and remainder, P = 24

P = q×r

24 = qr

qr = 24

r = 24/q           ----------------   (ii)

Sum of quotient and remainder, S = 10

S = q + r

10 = q + r

q + r = 10

But from (ii), we have r = 24/q

Now, we have,

q + 24/q = 10

(q² + 24)/q = 10

q² + 24 = 10q

q² - 10q + 24 = 0

q² - 6q - 4q + 24 = 0

q(q - 6) - 4(q - 6) = 0

(q - 6)(q - 4) = 0

q = 6, 4

Putting value of q in (ii), we get

r = 24/q = 4, 6

The values of quotient and remainder are (6 and 4) and (4 and 6).

Now, from (i), we have

Dividend = Divisor × Quotient + Remainder

Taking quotient, q = 6 and remainder, r = 4, we have

Dividend = 5 × 6 + 4

               = 30 + 4 = 34

Taking quotient, q = 4 and remainder, r = 6, we have

Dividend = 5 × 4 + 6

                = 20 + 6 = 26

Hence, the value of dividends is 34 and 26.

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