1)  Three persons M₁, M₂ and M₃ can complete a work in 15, 20 and 30 days respectively. Only two of these three work in any given day. But, the same two persons do not work for any two consecutive days. What is the least number of days in which the work is completed? 









































































































2)    How many three digit numbers lie between 200 and 500 in which 4 comes only one time?
A) 117
B) 135
C) 139
D) 143
Step 1: Range of Numbers
The three-digit numbers between 200 and 500 are from 200 to 499.
Step 2: Possible Hundreds Digits
The hundreds digit can be 2, 3, or 4.
Step 3: Case Analysis
Case 1: Hundreds digit is 2 or 3 (i.e., 200-299 or 300-399)
The hundreds digit is not 4, so 4 can only appear in the tens or units, and exactly once.
For each hundreds digit (2 or 3):
Place 4 in the tens place:
Hundreds: 2 or 3 (2 options)
Tens: 4 (fixed)
Units: Any digit from 0 to 9 except 4 (9 options)
Count: 2×1×9=18
Place 4 in the units place:
Hundreds: 2 or 3 (2 options)
Tens: Any digit from 0 to 9 except 4 (9 options)
Units: 4 (fixed)
Count: 2×9×1=18
Total for 2 and 3 as hundreds digit: 18+18=36
Case 2: Hundreds digit is 4 (i.e., 400-499)
4 comes in the hundreds, but should not appear again in tens or units.
Hundreds: 4 (1 option)
Tens: Any digit from 0 to 9 except 4 (9 options)
Units: Any digit from 0 to 9 except 4 (9 options)
But we want 4 to appear only once (in hundreds place), so tens and units cannot be 4.
Count:1×9×9=81
Step 4: Total Count
Total = Numbers with one 4 in tens/units (hundreds = 2, 3) + Numbers with one 4 in hundreds (hundreds = 4)
Total = 36 + 81 = 117
Ans)  A) 117