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27 Jul 2026, 19:00
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B
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Difficulty:
65%
(hard)
Question Stats:
53% (03:02) correct
47%
(02:44)
wrong
based on 62
sessions
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Mrs. Sharma has a few chocolate candies which she wants to distribute among her five grand-daughters. If she distributes the candies among them in the ratio of 1 : 4 : 5 : 7 : 9, then 1 candy is left out. If she distributes the candies in the ratio of 2 : 3 : 3 : 4 : 5, then 3 candies are left out. However, if she distributes the candies among them in the ratio of 1 : 2 : 3 : 7 : 8, then no candies are left over. What is the minimum number of candies that any of the five grand-daughters can receive in any of the three cases?
A. 3
B. 4
C. 5
D. 6
E. 12
A. 3
B. 4
C. 5
D. 6
E. 12
27 Jul 2026, 22:36
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1x:4x:5x:7x:9x with one left will be 26x+1
2y:3y:3y:4y:5y with three left will be 17y +3
and
1z:2z:3z:7z:8z with no left will be 21z , multiples of 21 are 21,42,. 105 etc, which satisfies the condition 26x+1 and 17y + 3 is 105 ( 26 * 4 +1 , 17*6+3)
leat cookies will be 1*4 = 4 in 1st case and 2*6 = 12 in second case
ans 4 option B
2y:3y:3y:4y:5y with three left will be 17y +3
and
1z:2z:3z:7z:8z with no left will be 21z , multiples of 21 are 21,42,. 105 etc, which satisfies the condition 26x+1 and 17y + 3 is 105 ( 26 * 4 +1 , 17*6+3)
leat cookies will be 1*4 = 4 in 1st case and 2*6 = 12 in second case
ans 4 option B
27 Jul 2026, 22:42
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ANs - B
add the ratios
1:4:5:7:9 = 26K leaves remainder 1
2:3:3:4:5 = 17K " " 3
1:2:3:7:8 = 21K " " 0 this means the total no of candies is a multiple of 21
taking total as 105 = and when diving by 26 leaves remainder of 1 and on diving by 17 leaves remainder 1
to find the min no if candies any of them can have put the value in the ratio i.e 1:2:5:7:9 = 26K, subtracting 1 from 105 to 104, this gives us min 4 in this case.
taking case 2 , 2:3:3:4:5=17k , subtracting 3 from 105 to 102, this gives min 12
taking case 3, this gives min 5 . so the min no of candies that any of the five can get is 4
add the ratios
1:4:5:7:9 = 26K leaves remainder 1
2:3:3:4:5 = 17K " " 3
1:2:3:7:8 = 21K " " 0 this means the total no of candies is a multiple of 21
taking total as 105 = and when diving by 26 leaves remainder of 1 and on diving by 17 leaves remainder 1
to find the min no if candies any of them can have put the value in the ratio i.e 1:2:5:7:9 = 26K, subtracting 1 from 105 to 104, this gives us min 4 in this case.
taking case 2 , 2:3:3:4:5=17k , subtracting 3 from 105 to 102, this gives min 12
taking case 3, this gives min 5 . so the min no of candies that any of the five can get is 4
Bunuel
