Question

When 5075, 3584 and 2732 are divided by the greatest number d , the remainder in each case is r. Then
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what is the value of (3d - 2r)?
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Answer 1

Answer:

we know that,

The greatest number that will divide x, y and z leaving the same remainder in each case is = HCF of (x - y), (y - z) and (z - x).

So,

Difference between given numbers is :-

→ 3584 - 2732 = 852.

→ 5075 - 3584 = 1491.

→ 5075 - 2732 = 2343 .

Than, Prime factors of 852 , 1491 and 2343 are :-

→ 852 = 2 * 2 * 3 * 71

→ 1491 = 3 * 7 * 71

→ 2343 = 3 * 11 * 71

HCF = 3 * 71 = 213 = d.

Therefore,

→ Remainder in each case is :-

→ 5075/213 = 176 = r.

→ 3584/213 = 176 = r.

→ 2732/213 = 176 = r.

Hence,

→ (3d - 2r)

→ 3*213 - 2*176

→ 639 - 352

→ 287 (Ans.)

Answer 2

Given :  5075, 3584 and 2732 are divided by the greatest number d , the remainder in each case is r.

To Find :  value of (3d - 2r)

Solution:

5075 =  ad + r

3584 = bd + r

2732 = cd + r

=> 5075 - 3584   = (a - b)d  =  1491

   3584 - 2732  =   (b - c)d   =   852

 

1491 = 852 * 1  +  639

852 = 639 * 1 + 213

639  = 213 * 3

213 is  d

5075 =  23 x 213  +176

3584 = 16*213 +176

2732 = 12 * 213 + 176

d = 213

r = 176

3d - 2r

= 3 *(213) - 2(176)

= 639 - 352

= 287

value of (3d - 2r)  = 287

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