Please show me the technique of these two ratio and percentage arithmetical problems without the use of calculator:

Question

1. The price of an item decreases 16 2/3 % (50/3 % or 16.67%), so that 5 extra quantities of the items can be bought for 75 $. How much is the current price for each dozen (12) of the items?
2. Two numbers are in the ratio 4:3, which of these four options cannot be the sum of these two numbers:

A. 112, B, 154, C. 178 D. 182.

I have the answers, (1. 30 $, 2 178, provided the answers are accurate, not sure), but I need the Technique to solve these Without a Calculator.

Answer 1

It's given two numbers have a ratio of 4:3

If the scale factor is "x", then numbers are 4x and 3x respectively.

Sum = 4x + 3x = 7x

Sum of these two numbers must be evenly divided by "7".

112/7 = 16, 154/7 = 22, 178/7 => does not divide evenly, 182/7 = 26

Answer: 178