Question

17. Atrader selling eggs in a village had a quarrel with a man who pulled
down the egg basket breaking all the eggs. The trader appealed to the
Panchayat for compensation from the offender. When the Panchayat asked
the trader how many eggs were broken, the trader replied,
If counted in pairs, one will be left;
If counted in threes, two will be left;
If counted in fours, three will be left;
If counted in fives, four will be left;
If counted in sixes, five will be left;
If counted in sevens, nothing will be left;
And my basket can contain not more than 150 eggs.
Question: How many eggs did the trader have?​

Answer 1

Answer:

140 EGGS

Step-by-step explanation:

Answer 2

Answer:

Let there are x eggs in the basket.

Then, x = 7 × q1 + 0 [As number is completely divisible by 7]

x = 6 × q2 + 5

x = 5 × q3 + 4

x = 4 × q4 + 3

x = 3 × q5 + 2

x = 2 × q6 + 1

Now, see the number is divisible by 7 and also the number of eggs are less than 150.

Consider the number less than 150 and divisible by 7:

147, 140, 133, 126, 119, 112, 105, 98,.....14, 7.

From these numbers, we see that 119 in divisible by 7.

Also 119 leaves remainder 5 when divided.

Also, the remainder by 6 is 4 when it is divided by 5.

It leaves remainder 3 when divided by 4.

It leaves the remainder 2 when divided by 3 and leaves the remainder 1 when divided by 2.

Hence, the number of eggs in the basket were 119.

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Step-by-step explanation: