from a basket of mango counted in two's there was one extra , counted in three's there was two extra , counted in four's there was three extra , counted in five's there was four extra, counted in six's there was five extra.but counted in sevens there was no extra. At least how many mangoe's were there in the basket ?
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Let the number of mangoes be x.
when x ÷ 2 leaves remainder as 1.
when x ÷ 3 leaves remainder as 2.
when x ÷ 4 leaves remainder as 3.
when x ÷ 5 leaves remainder as 4.
when x ÷ 6 leaves remainder as 5.
when x ÷ 7 leaves remainder as 0.
⇒ x is divisible by 7.
The remainder in each case is 1 less than the divisor.
⇒ (x + 1) is the LCM of 2, 3, 4, 5 and 6.
LCM of 2, 3, 4, 5 and 6 = 60.
If x + 1 = 60, then x = 59.
But 59 is not divisible by 7.
If x + 1 = 120, then x = 119.
119 is divisible by 7 also it satisfies all the conditions.
Hence the number of mangoes = 119.
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