 Hello and welcome to the session. In this session, we will discuss the following question. And the question says if 1 upon p is equal to q r upon q plus r, make r the subject of the formula. Hence calculate r if p is equal to 1 upon 7, u is equal to 5 and 1 upon 4. Let's start the solution now. We are given this formula and we have to make r the subject of the formula. So the given formula is 1 upon p is equal to q r upon q plus r. Now to make r the subject of the formula, we will express r in terms of other variables that is p and q. First we will do cross multiplication. So on cross multiplying we get this implies q plus r is equal to p q r. Now we will transpose r to the right hand side. So this implies q is equal to p q r minus r. This implies q is equal to taking r common we get r into p q minus 1 the whole or we can say that r into p q minus 1 the whole is equal to q. This implies r is equal to q upon p q minus 1. So in this way we have made r the subject of the formula. Therefore the required formula with subject r is equal to q upon p q minus 1. So this is the answer. Now we have to calculate r if p is equal to 1 and 1 by 7 and q is equal to 5 and 1 by 4. So when p is equal to 1 and 1 by 7 this is equal to 8 upon 7 and q is equal to 5 and 1 by 4 which is equal to 21 by 4. This implies r is equal to substituting the values of p and q in this formula we get q that is 21 by 4 upon e e to q that is 8 by 7 into 21 by 4 minus 1. Now in the denominator 7 3 times is 21 and 3 2 times is 8. So this implies r is equal to 21 by 4 upon 6 minus 1. This implies r is equal to 21 by 4 into 1 upon 5. This implies r is equal to 21 upon 20 which is equal to 1 and 1 by 20. Hence r is equal to 1 and 1 by 20 and this is the final answer. With this we end our session. Hope you enjoyed the session.