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.
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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!!
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