 Hello and welcome to the session. In this session we discussed the following question which says the ratio of the prices of two articles was 16 is to 23. Two years later when the price of the first article rose by 10% and that of the second by 477 dollars the ratio of the prices became 11 is to 20. Find the original prices of the two articles. Let's proceed with the solution now. We need to find the original prices of the two articles according to the conditions given in the question. So first of all we assume let the original prices of the two articles be 16x dollars and 23x dollars respectively. Since in the question it's given that the ratio of the prices of two articles was 16 is to 23. So we have assumed the original prices of the two articles as 16x dollars and 23x dollars. Now the next condition given in the question is that two years later price of the first article rose by 10% and that of the second by 477 dollars. And then the ratio of the prices became 11 is to 20. So next we have two years later price of the first article is equal to 16x plus 10% of 16x dollars. Since it's given in the question that the price of the first article rose by 10% so after two years or two years later the price of the first article would be equal to 16x plus 10% of 16x dollars. So this is equal to 16x plus 10 upon 100 into 16x dollars which further is equal to Now here this 0 and 0 cancels and 2 8 times is 16 5 times is 10 so we get this is equal to 16 into 5 which becomes 80x plus 8x this whole upon 5 dollars and so we get this equal to 88x upon 5 dollars. So two years later price of the first article would be equal to 88x upon 5 dollars. Next in the question we are given that two years later the price of the second article rose by 477 dollars. So now two years later price of the second article is given by 23x plus 477 dollars. Also in the question we have that two years later when the price of first article rose by 10% and that of second by 477 dollars then their ratios become 11 is to 20. So now we have according to the question 88x upon 5 dollars is to 23x plus 477 dollars is equal to 11 is to 20. This means 88x upon 5 this whole upon 23x plus 477 is equal to 11 upon 20. Next we have 88x upon 5 into 23x plus 477 the whole is equal to 11 upon 20. Now this can be further written as 88x upon 11 into 23x plus 477 the whole is equal to 5 upon 20. Then 11 8 times is 88 and 5 4 times is 20 so we get 8x upon 23x plus 477 is equal to 1 upon 4. Next we cross multiply and we get 8 multiplied by 4 which is 32x is equal to 23x plus 477. Now transposing 23x to the left hand side we get 32x minus 23x is equal to 477 this gives us 9x is equal to 477. Now to get the value for x we divide both sides by 9 so we have 9x upon 9 is equal to 477 upon 9. This 9 cancels with 9 and here 9 53 times is 477 this gives the value of x as 53. Now that we have the value for x so we can easily find out the original price of the first article equal to 16x dollars. So we put the value of x here to get the original price of the first article so this means the original price of the first article is equal to 16 into 53 dollars. And this is equal to 848 dollars so we have original price of the first article is 848 dollars. Now next we find out the original price of the second article is equal to as we had assumed the original price of the second article to be 23x dollars. So we put the value of x here to get the original price of the second article so this is given by 23 multiplied by 53 dollars which is equal to 1219 dollars. This is the original price of the second article. So finally we get the original price of the first article as 848 dollars and original price of the second article as 1219 dollars. So these are the two answers this completes the session hope you have understood the solution of this question.