A trader with a basket of eggs find that if he sells 3 eggs at a time there is only 1 egg left. If he sells 4 eggs at a time then there is again 1 egg left. However, if the trader sells 7 eggs at a time, there are no eggs left. If the capacity of the basket is 100 eggs, find how many eggs are in basket? Explain with reasoning.

Open in App

Solution

We know that the LCM of 3 and 4 is 12. We have also been given that the maximum capacity of the egg basket is 100.

Lets list down the multiples of 12 till the number reaches 100.
12, 24, 36, 48, 60, 72, 84, 96

To leave a remained with 3 as well as 4, these numbers list above need to be one more; so we get the new numbers as follows:
13, 25, 37, 49, 61, 73, 85, 97.

The given statement also states that when 7 eggs are selected, no eggs remain. That mean we are looking for a number that is divisible by 7.

From 13, 25, 37, 49, 61, 73, 85, 97, we see that only 49 matches all the three criteria.

Hence the total number of eggs in the basket is 49.

Suggest Corrections

Similar questions

Q. A boy was carrying a basket of eggs. He fell down and some of the eggs were broken. The boy has 10 eggs left with him. When asked by his mother, how many eggs were broken, the boy could not recall. However, he racalled that when 1 egg was left, he counted 3 at a time. When counted 4 at a time, 1 egg was left and when counted 5 at a time, no egg was left. Minimum how many eggs were broken?

Q. An egg vendor calls on his first customer and he sells half his eggs and half an egg. To the second customer, he sells half of what he has left with and half an egg, and to the third customer, he sells half of what he was then left with and half an egg. However, he did not break any egg. If in the end, the vendor was left with three eggs, how many did he have initially ?

A trader was moving along a road selling eggs. An idler who didn’t have much work to do, started to get the trader into a wordy duel. This grew into a fight, he pulled the basket with eggs and dashed it on the floor. The eggs broke. The trader requested the Panchayat to ask the idler to pay for the broken eggs. The Panchayat asked the trader how many eggs were broken. He gave the following response: If counted in pairs, one will remain; If counted in threes, two will remain; If counted in fours, three will remain; If counted in fives, four will remain; If counted in sixes, five will remain; If counted in sevens, nothing will remain; My basket cannot accomodate more than 150 eggs. So, how many eggs were there?

Q. An egg vendor calls on his first customer and sells half his eggs and half an egg. To the second customer, he sells half of what he has left with and half an egg, and to the third customer, he sells half of what he was then left with and half an egg. However, he did not break any egg. If in the end, the vendor was left with three eggs did he have initially?

Q. A shopkeeper has certain number of eggs of which

5 %

are found to be broken. He sells

93 %

of the remainder and still has

266

eggs left. How many eggs did he originally have?

Join BYJU'S Learning Program