This activity allocated to class IV during Get-Set-Go was Marble in Spoon Race. The class teacher of IV-Z bought 10 marbles more than the total number of students in her section. The shopkeeper gave her 30 extra marbles for free as well. On the way, the packet of free marbles got torn and a few marbles were lost. To know the exact number of marbles, she gave the chance of counting to both boys and girls of the class. The girls tried to count by counting the marbles into piles of 4, and were left over with 3 marbles. The boys tried to count by putting the marbles into piles of 7, and were left over with 1 marble. If the class strength is 40, could you calculate, how many marble does class IV -Z have ?
Answers
Answer:
71 marbles
Step-by-step explanation:
Since there are 40 students in the class and the teacher bought 10 extra marbles therefore total number of marbles including the 30 free marbles = 80
Since the packet containing free marbles was torn, therefore the minimum number of available marbles = 40
Now we want a number between 40 and 80 which when divided by 4 leaves remainder 3 and when divided by 7, leaves remainder 1. We need to see multiples of 7 greater than 40 and less than 80, increase it by 1 so that it leaves remainder 1 when divided by 7 and check if it leaves remainder 3 when divided by 4
By trial and error
7 x 7 = 49, 49+1 = 50, 50 on dividing by 4 leaves remainder 2
7 x 8 = 56, 56+1 = 57, 57 on dividing by 4 leaves remainder 1
7 x 9 = 63, 63+1 = 64, 64 on dividing by 4 leaves remainder 0
7 x 10 = 70, 70+1 = 71, 71 on dividing by 4 leaves remainder 3
Thus the answer is 71
Answer:
There are 40 students in the class
The teacher bought 10 extra marbles
Therefore total number of marbles including the free 30 marbles = 40+10+30= 80
The packet containing free marbles was torn
The minimum number of available marbles = 40
Now a number between 40 and 80 which when divided by 4 leaves remainder 3 and when divided by 7, leaves remainder 1. We need to see multiples of 7 greater than 40 and less than 80, increase it by 1 so that it leaves remainder 1 when divided by 7 and check if it leaves remainder 3 when divided by 4
Therefore,
7 x 7 = 49, 49+1 = 50, 50 on dividing by 4 leaves remainder 2
7 x 8 = 56, 56+1 = 57, 57 on dividing by 4 leaves remainder 1
7 x 9 = 63, 63+1 = 64, 64 on dividing by 4 leaves remainder 0
7 x 10 = 70, 70+1 = 71, 71 on dividing by 4 leaves remainder 3
Hence the answer is 71