Question

20) If a number is divided by 38 the remainder is 31 and if it is divided by 50 the remainder is 43. Find smallest such
number.​

Answer 1

Answer:

Let us see the relation between the pairs of numbers if there is any:

20 - 14 = 6

25 -19 = 6

35 - 29 = 6

40 - 34 = 6.

The difference is 6, so there is a pattern

Next find the LCM of 20, 25, 35 and 40.

20 = 2x2x5

25 = 5x5

35 = 5x7

40 =2x2x2x5

So LCM = 2^3x5^2x7 =1400

The deduct 6 from 1400 to get 1394, which is the required number.

Check: 1394/20 = 69Q + 6R

1394/25 = 55Q + 19R

1394/35 = 39Q + 29R

1394/40 = 23Q + 34R

Step-by-step explanation:

hope it helps you!!