Question

When a number X is divided by 90 or 60 the reminders are 82 and 52 respectively. Dertamine the value of X

Answer 1

Answer:

52

Step-by-step explanation:

In general:

a = b×q + r

Where,

a is the number which is divided by 'b' divisor and the 'q' quotient and 'r' reminder come.

Now,

According to 1st condition:

x = 90×q + 82 ---------------(1)

Similarly,

x = 60×p + 52 ---------------(2)

(1) = (2):

90×q + 82 = 60×p + 52

82 - 52 = 60×p - 90×q

30 = 60×p - 90×q

Divide whole equation by 30, we get:

1 = 2× p - 3×q

1 + 3×q = 2×p --------------(3)

Put (3) in (2):

x = 60×(1 + 3×q) + 52

x = 60 + 180×q +52

x = 112 + 180×q

180×q = x - 112

q = (x - 112)/180 -------------(4)

Put (4) in (1):

x = 90×(x - 112)/180 + 82

x = (x - 112)/2 +82

x = {(x - 112) + 164}/2

2x = x - 112 + 164

2x - x = 164 - 112

x = 52

Therefore the number is 52.

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