Question

"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"
solve this puzzle

Answer 1

Let there are x eggs in the basket.Then, x = 7 × q 1 + 0 [As number is completelydivisible by 7]x = 6 × q 2 + 5x = 5 × q 3 + 4x = 4 × q 4 + 3x = 3 × q 5 + 2x = 2 × q 6 + 1Now, see the number is divisible by 7 and alsothe number of eggs are less than 150.Consider the number less than 150 and divisibleby 7:147, 140, 133, 126, 119, 112, 105, 98,.....14, 7.From these numbers, we see that 119 in divisibleby 7.Also 119 leaves remainder 5 when divided.Also, the remainder by 6 is 4 when it is dividedby 5.It leaves remainder 3 when divided by 4.It leaves the remainder 2 when divided by 3 andleaves the remainder 1 when divided by 2.Hence, the number of eggs in the basket were119

Answer 2

119 eggs in total that he have in the basket
because it is that multiple of 7 that satisfies in all these conditions