question_answer

A trader was moving along a road selling eggs. An idler who did not 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, then eggs are broken. The trader requested to the panchayat to say the idler to pay for broken eggs. (i) The panchayat asked the trader how many eggs were in this basket? He gave the following response If counted in pairs, one will remain. If counted in 3, two will remain. If counted in 4, three will remain. If counted in 5, four will remain. If counted in 6, five will remain, if counted in 7, nothing will remain, my basket cannot accomodate more than 150 eggs. So, how many eggs were there? (ii) Which Mathematical concept will be used for solving the question? (iii) What value of the trader shows in the question?  

Answer:

(i) Let the number of eggs  given] If counted in 7, nothing will remain; for some natural number If counted in 6, 5 will remain; for some natural number q                                            (1) If counted in 5, 4 will remain; for some natural number w                                        (2) If counted in 4, 3 will remain; for some natural number s If counted in 3, 2 will remain; for some natural number t If counted in pairs, one will remain; for some natural numbers That is, in each case, we have a and a positive integer b take values 7, 6,5, 4, 3 and 2 respectively, which divides a and leaves a remainder r (r is 0, 5, 4, 3, 2 and 1, respectively) which is smaller than b. We must look for the multiple of 7 which satisfy all the conditions. By trial and error (using the concept of LCM), we will find, he had 119 eggs. (ii) Euclid's division lemma is used to slove the question.    (1) (iii) The value of the trader in the question is honesty.      (1)