OE

As on diving 𝑛 apples among an odd number of boxes with 5 apples in each box, 2
apples are left out. This implies that 𝑛 is an odd number which on dividing by 5
leaves a remainder 2.
Hence, using dividend, divisor, and remainder relationship; the possible values of 𝑛
will be;
𝑛 = (5 × 𝑜𝑑𝑑) + 2
If, in the above equation, odd number = 1, 𝑛 = 7
If odd number = 3, 𝑛 = 17
If odd number = 5, 𝑛 = 27 and so on.
In each case, when number of apples 7, 17, 27, …., divided by 10 remainder is 7.
Or, 𝑛 = (5 × 𝑜𝑑𝑑) + 2 =
Or, 𝑛 = 5(2𝑛 + 1) + 2 (As odd numbers can be expressed as2𝑛 + 1 )
Or, 𝑛 = 10𝑛 + 5 + 2 = = 10𝑛 + 7
Now, if each box is filled with only 10 apples instead of 5, this implies that we need
to divide 𝑛 by 10. Hence when we divide 𝑛 by 10, we can see that the remainder will
be 7.
Ans. (7)