M4maths Previous Puzzles

03 Oct 2022 Permutation & Combinations

In an inning of a T20 match, a team scores 140 runs only with the help of 4s and/or 6s. In how many ways can a team score these runs ?

OPtion

1) 18
2) 10
3) 12
4) 14
5) 16
6) 20
7) 13
8) 15
9) 9
10) None of these

Solution

Let x 4's and y 6's are scored in an inning, then 4x + 6y = 140
Here (x,y) can have values (2,22) (5,20) (8,18), (11,16) (14,14) (17,12) (20,10) (23,8) (26,6) (29,4) (32,2) (35,0), Total 12
Thus in 12 ways 140 runs can be scored with the help of 4s and 6s only.

Correct Option: 3 Best Solution (3)

G.S.Kantharao   2 years AGO

4x+6y=140
(X,y)=(35,0),(32,2),(29,4),(26,6),(23,8),(20,10),(17,12),(14,14),(11,16),(8,18),(5,20),(2,22)
are the possible ways. So totally 12 ways.
My option is 3👈

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AAKASH RAWAT   2 years AGO

Team scores = 140 runs
Possible Arrangements:
Fours (4s). Six (6s)
35 0
32 2
29 4
26. 6
23. 8
20. 10
17. 12
14. 14
11. 16
8. 18
5. 20
2. 22
Total no of ways - 12 ways

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RAMADURAI NATESAN   2 years AGO

LCM of 4 and 6 = 12.
Total no. of 12 0r its multiples in tables of 4 and 6 between 4 and 140 = 11. In one way, 140 runs cld be taken by all 4s.
Thus in 11 + 1 = 12 ways team can score 140 runs

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