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02 Apr 2020, 09:59
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A
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Difficulty:
45%
(medium)
Question Stats:
67% (02:33) correct
33%
(02:27)
wrong
based on 164
sessions
History
Date
Time
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Not Attempted Yet
A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio:
A. 1 : 1
B. 8 : 7
C. 4 : 3
D. 6 : 5
E. 7 : 5
A. 1 : 1
B. 8 : 7
C. 4 : 3
D. 6 : 5
E. 7 : 5
03 Apr 2020, 00:14
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Bunuel
Let the common ratio be x for popcorn packets, so L,S and J are 7x, 17x and 16x and total is 7x+16x+17x=40x
Similarly if common ratio for chips packet is y, total is 6y+15y+14y=35y.
Given that 40x=35y...........\(x\frac{}{y}=\frac{35}{40}=\frac{7}{8}\)
Now we are looking for value of \(\frac{16x}{14y}=\frac{8}{7}*\frac{x}{y}=\frac{8}{7}*7\frac{}{8}=1\)
so 1:1
A
03 Apr 2020, 03:48
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A ratio question like this tests your knowledge of multiples. That’s primarily because the ratio terms cannot represent a fraction here (you cannot sell fractional number of packets) and hence the understanding is that the ratio terms represent the multiples of the corresponding numbers.
For popcorn, the number of large, super and jumbo packets are in the ratio of 7:17:16. Adding all the ratio terms, we get 40. Therefore, the total number of popcorn packets are a multiple of 40.
For chips, the number of large, super and jumbo packets are in the ratio of 6:15:14. Adding all the ratio terms, we get 35. The total number of chips packets must therefore be a multiple of 35.
Since both the totals are same, this now becomes an LCM problem. The LCM of 35 and 40 is 280.
Of 280 total popcorn packets, number of jumbo packets = 16 / 40 * 280 = 16 * 7 = 112.
Of 280 chips packets, number of jumbo packets = 14 / 35 * 280 = 14 * 8 = 112.
The required ratio is 1:1. The correct answer option is A.
Hope that helps!
For popcorn, the number of large, super and jumbo packets are in the ratio of 7:17:16. Adding all the ratio terms, we get 40. Therefore, the total number of popcorn packets are a multiple of 40.
For chips, the number of large, super and jumbo packets are in the ratio of 6:15:14. Adding all the ratio terms, we get 35. The total number of chips packets must therefore be a multiple of 35.
Since both the totals are same, this now becomes an LCM problem. The LCM of 35 and 40 is 280.
Of 280 total popcorn packets, number of jumbo packets = 16 / 40 * 280 = 16 * 7 = 112.
Of 280 chips packets, number of jumbo packets = 14 / 35 * 280 = 14 * 8 = 112.
The required ratio is 1:1. The correct answer option is A.
Hope that helps!
