### Graphs Class 10th Mathematics Tamilnadu Board Solution

##### Question 1.A bus travels at a speed of 40 km/hr. Write the distance-time formula and draw the graph of it. Hence, find the distance travelled in 3 hours.Answer:Suppose a body X travels a at a speed of S km/h for T hours then the distance covered by him will be D and its given asD = ST kmHere speed of bus, s = 40 km/hrTravel time , t = 3hrsSo using this we can find a set of distance and put them in graph to find the exact distance travelled by the bus  to know the distance covered by the bus at three hours draw a line parallel to Y-axis from X = 3 to the curve and from the intersecting point of that line and the curve draw another line parallel to X-axis and the point at which the line intersect the Y-axis will give the distance coveredso from the graph it’s clear that as the bus was running for 3 hrs. and it covered a distance of 120 km.Question 2.The following table gives the cost and number of notebooks bought. Draw the graph and hence (i) find the cost of seven note books.(ii) How many note books can be bought for ₹165.Answer: From the above it’s clear that y = 15 × XPutting the above value in graph we will find (i) To find the cost of 7 books draw a line parallel to Y-axis from X = 7 to the curve and from the intersecting point of that line and the curve draw another line parallel to X-axis and the point at which the line intersect the Y-axis will give the cost of 7 books.so from the graph cost of 7 books is found to be ₹105(ii) to find the number of book that can be purchased at a cost of 165 draw a line parallel to X-axis from Y = 165.from the point at which the line intersect the curve draw another line parallel to Y-axis and the point at which the line intersect x-axis will give the number of book.so we can buy 11 note booksQuestion 3. Draw the graph for the above table and hence find(i) the value of y if x = 4(ii) the value of x if y = 12Answer:Using the data we can draw a graph (I) TO FIND THE VALUE OF the value of y if x = 4, draw a line parallel to Y-axis from X = 4 to the curve and from the intersecting point of that line and the curve draw another line parallel to X-axis and the point at which the line intersect the Y-axis will give the value of Y ay X = 4.so from the graph at X = 4 Y is found to be 8(II) to find the value of X at Y = 12 draw a line parallel to X-axis from Y = 12 and from the point at which the line intersect the curve draw another line parallel to Y-axis and the point at which the line intersect x-axis will give the value of X.so we find at Y = 12 Xis found to be 6Question 4.The cost of the milk per liter is ₹15. Draw the graph for the relation between the quantity and cost. Hence find(i) the proportionality constant.(ii) the cost of 3 litres of milk.Answer:(i) k = 15 (ii) ₹45Let the cost of milk be Y and X be the quantity of milk in liter. As it’s given that cost per one liter is 15rs so increase in quantity will increase the cost of milk. So it’s a direct proportionMathematically,Y = KXWhere K is the constant of proportionalitySo we can draw a table so from the graph it’s clear that y = kx = 15xProportionality, k = 15We can draw a graph using the table given To find the cost of 3 liter milk we have to draw a line parallel to Y-axis at X = 3 then from the intersection point of that parallel line and the curve draw another line parallel to X-axis so the point of intersection of that line and Y-axis will give the cost of 3 liter of milk.From the graph its clear that cost of 3 liter is 45 RS.Question 5.Draw the Graph of xy = 20, x, y > 0. Use the graph to find y when x = 5, and to find x when y = 10.Answer:We are given that xy= 20⇒ y = (20/x)We can find different value of Y by taking values of x between 1 and 10  From the graph we get that at x = 5, y = 4, and to find y = 10, x = 2Question 6. Draw graph for the data given in the table. Hence find the number of days taken by 12 workers to complete the work.Answer:We can construct a graph using the data given To find the number of days taken by 12 worker to complete the work draw a line parallel to Y-axis from X = 12 to the curve and from the intersecting point of that line and the curve draw another line parallel to X-axis and the point at which the line intersect the Y-axis will give the value of Y at X = 12.so from the graph at X = 12 Y is found to be 26

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