 Hello and welcome to the session. In this session we discuss the following question which says, a tree casts a shadow of length 10 meters at a time when a pole 12 meters high casts a shadow of length 15 meters, find the height of the tree. We know when we are given four numbers a, b, c, d and they are in proportion that is a is to b is proportional to c is to d then the product of the extremes that is a multiplied by d is equal to the product of the means which is b, c. So, a, d is equal to b, c when we are given the four numbers a, b, c, d are in proportion. So, this is the key idea that we use in this question. Now let's see the solution of the question. We are given the length of the shadow of the tree is given as 10 meters then we have the height of the pole is 12 meters and we are also given that the length of the shadow of the pole is given as 15 meters and we have to find the height of the tree. Now since we have that the tree casts a shadow at a time when the pole casts a shadow. So, this means that the height of the tree length of the shadow of the tree is proportional to height of the pole the length of the shadow of the pole. Height of the tree length of the shadow of the tree height of the pole and length of the shadow of the pole are in proportion. We assume that the height of the tree be equal to x meters we put the values of height of the tree length of the shadow of the tree height of the pole and length of the shadow of the pole here. So, we get x is to 10 is equal to 12 is to 15 since we are in proportion so we put the equal to sign here. Now since we know when the four numbers are in proportion so the product of extreme is equal to the product of the means and so here we have product of the extreme which is 15 and x which is 15 x is equal to the product of the means that is 10 and 12 equal to 120 to get the value of x we divide both sides by 15. 15 cancels with 15 and 15 8 times is 120 therefore we get x is equal to 8 and we are taking the height of the tree to be equal to x meters so we say height of the tree is equal to 8 meters. So, this is our final answer. This completes this session. Hope you have understood the solution of this question.