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There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs. 100 per metre it will cost the village panchayat Rs. 75000 to fence the plot. What are the dimensions of the plot?

Solution Let the length of the rectangular plot be 11x Let the breadth of the rectangular plot be 4x. Rate of fencing per metre = ₹100... View Article

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression C = 2πr ,where r is the radius of the circle

(a) Radius = Diameter/2 = 2.8/2 cm = 1.4 cm Circumference of semi-circle = ∏.r = (22/7)×1.4 = 4.4 Circumference of semi-circle is... View Article

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. i. 252 ii. 2925 iii. 396 iv. 2645 v. 2800 vi. 1620

Solution (i) 252 252 = 2 × 2 × 3 × 3 × 7 = (2 × 2) × (3 × 3) × 7 7 cannot be paired.... View Article

Give one example of a situation in which (i) the mean is an appropriate measure of central tendency. (ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

(i) Mean marks obtained by a student in various subjects. The entries in this case will be close to each other. Therefore, the mean will be... View Article

Sides of triangles are given below. Determine which of them are right triangles? In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm

(i) Given: 7cm, 24cm, 25cm (25)2= 25 * 25 = 625 ∴The are sides of a right ∆ and hypotenuse = 625 (ii) Given: 3cm, 8cm, 6cm... View Article

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. How much paper of each shade has been used in it?

As the area of the kite is in the square, its area will be Area of kite = 1/2×(diagonal)2 = 1/2×32×32 = 512 cm2... View Article

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. i. 402 ii. 1989 iii. 3250 iv. 825 v. 4000

Solution (i) 402 We obtained the remainder as 2 2 is the least required number to be subtracted from 402 to get a perfect square New... View Article

I have a total of Rs. 300 in coins of denomination Rs. 1, Rs. 2 and Rs. 5. The number of Rs. 2 coins is 3 times the number of Rs. 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Solution Let number of ₹5 coins be ‘C’. Number ₹2 coins = 3C Number of ₹1 coins = (160 – 4C) Value of ₹5 coins= C... View Article

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m ² is Rs. 4.

Given Length of one diagonal, d1 = 45 cm and d2= 30 cm Find out We have to find the total cost of polishing the tile of if the... View Article

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in fig. Eight such spheres are used forth is purpose, and are to be painted silver. Each support is a cylinder of radius 1.5cm and height 7cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint costs 5 paise per cm².

Given Diameter of wooden sphere = 21 cm Radius of wooden sphere, r = (21/2) cm = 10.5 cm Find out We have to find out the cost of... View Article

A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Solution Let ABCD be the plot of the land of the shape of a quadrilateral Construction Join the diagonal BD. Draw AE parallel to BD.... View Article

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

From the given conditions, we observed that Niharika posted the green flag at 1/4th of the distance AD i.e., (1/4 ×100) m = 25m from the... View Article

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot as shown in the Fig. The students are to sow the seeds of flowering plants on the remaining area of the plot. (i) Taking A as origin, find the coordinates of the vertices of the triangle. (ii) What will be the coordinates of the vertices of triangle PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?

(i) On taking A as origin, coordinates of the vertices P, Q and R are, From figure: P = (4, 6), Q = (3, 2), R (6, 5) Now AD is the x-axis and AB... View Article

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig.) . Find the distance travelled by the balloon during the interval.

On redrawing the diagram we get From right ΔBEC, tan 30° = BE/CE 1/√3= 87/CE CE = 87√3 From right ΔADC,... View Article

In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig.) . Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ΔABC ≅ ΔDEF.

Given In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F... View Article

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Number of mangoes 50-52 53-55 56-58 59-61 62-64 Number of boxes 15 110 135 115 25 Solution The class intervals are not continuous and... View Article

The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

Frequency:- No. of students having the same blood group. Blood Group Number of Students (Frequency) A 9 B 6 O 12 AB 3 Total 30... View Article

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5 m long.

Solution The height of the pole and length of the shadow are in direct proportion. We know that 1 m = 100 cm 5 m 60 cm = 5×100+60 = 560... View Article

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Represent the situation algebraically and geometrically.

Let the cost of 1 kg of apples be ‘Rs. x’ And, cost of 1 kg of grapes be ‘Rs. y’ According to the given condition the... View Article

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

Given that The numbers of logs in rows are in the form of an A.P.20, 19, 18… From the given data First-term, a = 20 Common difference, d... View Article