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20 May 2022 : LCM & HCF
The ratio of sum to the LCM of two natural numbers is 12:35. If their HCF is 6, then the smaller number is
A, B and C together can complete certain work in 24 days. A and C together work twice as much as B while A and B together works four times the as much as C, then A alone can do the same work in
OPtion
1) 72 days
2) 120 days
3) 48 days
4) 30 days
5) 36 days
6) 180/7 days
7) 360/7 days
8) 90/7 days
9) 270/7 days
10) None of these
Solution
Let A, B and C can do the work in a, b and c days respectively.
Then, 1 day's work of A, B & C = 1/a + 1/b + 1/c = 1/24 ----(i)
1/a + 1/c = 2/b ----(ii)
1/a + 1/b = 4/c ----(iii)
Now subtracting (ii) from (i), we get 1/b = 1/72
Similarly subtracting (iii) from (i), we get 1/c = 1/120
Substituting values of 1/b and 1/c in (i), 1/a = 7/360
.'. A alone can do the work in 360/7 days.
Correct Option 7)