 Hello and welcome to the session. In this session we discussed the following question that says what number must be added to each of the numbers 9, 5, 12, 7 to get the numbers which are in proportion. We know that if A is to B is proportional to C is to D then the product of extremes that is A into D is equal to the product of the means that is B into C. This is the key idea for this question. Let's move on to the solution now. We take let the required number be equal to X that is we add X to each of the numbers 9, 5, 12 and 7 such that they are in proportion. So we have 9 plus X is to 5 plus X is proportional to 12 plus X is to 7 plus X. Now that these numbers are in proportion so product of extremes that is 9 plus X multiplied by 7 plus X is equal to the product of X which is 5 plus X into 12 plus X. Now this further gives us 63 plus 16 X plus X square is equal to 60 plus 17 X plus X square. Now X square, X square cancels on both the sides. We get 17 X minus 16 X is equal to 63 minus 60 which gives us X is equal to 3. So we have 3 must be added to each of the numbers 9, 5, 12 and 7 to get the numbers which are in proportion. Thus 3 is our final answer. This completes the session. Hope you have understood the solutions for this question.