ID : in-7-olympiad [1] Class 7 Olympiad For more such worksheets visit www.edugain.com Answer the questions (1) When 24 is added to 40 % of a number, it gives the number itself. Find the number. (2) If the perimeter of the following semi-circular shape is 180 cm, find its radius. (assume π = 22/7) (3) Tap A can fill a tank in 2 hours, while tap B can empty the full tank in 3 hours. If both taps are open together, how long will it take to fill an empty tank? (4) Among five friends, Meenakshi is taller than Joel, but not as tall as Akshiti. Ankur is taller than Usha but shorter than Joel. Who is the shortest in the group? (5) The first figure given below shows a wire in circular shape with the radius of 108 cm. Shyam cut out an arc from wire such that the arc makes an angle of 90 at the center. If this arc is again bent in circular shape as shown in the second picture, find the radius of the new circle. (6) What is the absolute value of a - 1, if a is greater than 1? (7) Sarika is walking in the south direction. After walking for 8 meters, she takes a right turn and walks for another 13 meters. She then takes a left turn and walks for 4 meters. She again takes a right turn and walks for another 3 meters. How far is she from the starting point? (8) If the average of numbers 36, 35, 34, 33, 32 and x is 40, find the value of x. (9) Aamir says, "Neha is the wife of the grandson of my mother". Who is Neha to Aamir?
(10) In the image given below, if the radius of all the large circles is r, then what is the radius of the inner smaller circle? ID : in-7-olympiad [2] (11) Find the sum of the following angles : P + Q + R + S + T + U =? (12) Find the missing term. (13) If lines AC and DE are parallel to each other, find the value of angle x.
ID : in-7-olympiad [3] Choose correct answer(s) from the given choices (14) If two days after tomorrow will be Sunday, when was Monday? a. Day before yesterday b. Two days before yesterday c. Today d. Yesterday (15) A dog is walking on the periphery of a regular polygon, as shown below. If it starts from point s, in the clockwise direction, which side will the dog reach after walking distance on the periphery? a. C b. D 18 25 c. E d. A 2017 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : in-7-olympiad [4] (1) 40 Let us assume the number to be x. 40 40 % of x = x = 40x 100 100 If we look at the question carefully, we will notice that the number(x) is equal to the sum of 24 and 40 % of x. So, it can be written as: x = 24 + 40x 100 x = 24 100 + 40x 100 2400 + 40x x = 100 By cross multiplying both the sides 100 x = 2400 + 40x 100 x - 40x = 2400 60x = 2400 x = 2400 60 x = 40 Therefore, the number is 40.
(2) 35 cm ID : in-7-olympiad [5] Let us assume that r and d are the radius and the diameter of the semi-circular shape, respectively. Diameter of the semi-circular shape = 2r Perimeter of the semi-circular shape = πr + d = πr + 2r = r(π + 2) = r( 22 7 + 2) = r( 22 7 + 2) = r( 22 + 14 7 ) = 36r 7 According to the question, the perimeter of the semi-circular shape is 180 cm. Therefore, 36r = 180 7 r = 180 r = 35 7 36 Thus, the radius of the semi-circular shape is 35 cm
(3) 6 hours ID : in-7-olympiad [6] If both taps are open together, then the time it will take to fill an empty tank is equal to the LCM of the time in which tap A fills the tank and tap B empties the full tank. Calculating the LCM of 2 and 3. All the prime factors of 2: 2 2 2 is a factor of 2 1 2 = 2 All prime factors of 3: 3 3 3 is a factor of 3 1 3 = 3 So, the LCM of 2 and 3 is = 3 2 = 6 Step 5 Therefore, the time it will take to fill the empty tank is 6 hours. (4) Usha Meenakshi is taller than Joel, this means Meenakshi is taller than someone. Meenakshi is not as tall as Akshiti, which means Akshiti is also taller than someone. Ankur is taller than Usha, this means Ankur is also taller than someone. Ankur is shorter than Joel, this means Joel is also taller than someone. Step 5 The only one left who is not taller than anyone is Usha.
(5) 27 cm ID : in-7-olympiad [7] Let us assume r is the radius of the circle, l is the length of the arc, and Ɵ is the angle of the arc at the center. According to the question, r = 108 cm Ɵ = 90 Length of the arc = Ɵr π l = Ɵ r...[by converting the angle into radian] 180 π = 90 180 = 54π cm 108 Let us assume that r 1 is the radius of the new circle. Length of the arc is equal to the circumference of the new circle. Therefore, 2πr 1 = 54π...[Since, the circumference of the new circle = 2πr 1 ] r 1 = 54π 2π r 1 = 27 cm Thus, the radius of the new circle is 27 cm. (6) a - 1 It is given that the value of a is greater than 1. So, the value of a - 1 will be positive. Hence, the absolute value of a - 1 is a - 1. (7) 20 meters
ID : in-7-olympiad [8] Let us use the conventional map directions while making the figure to represent the distances traveled by Sarika: Assuming Sarika started from point A and finally reached point E, the path traveled by Sarika can be drawn as below: Let us extend the segments ED and AB to meet at F as shown below: Here, AF = 8 + 4 = 12 EF = 13 + 3 = 16
ID : in-7-olympiad [9] By applying the Pythagorean Theorem, the distance between starting point A and ending point E: (AE) 2 = (AF) 2 + (EF) 2 (AE) 2 = 12 2 + 16 2 (AE) 2 = 144 + 256 (AE) 2 = 400 AE = 400 AE = 20 Therefore, Sarika is 20 meters from the starting point. (8) 70 If we look at the question carefully, we notice that the average of the numbers 36, 35, 34, 33, 32 and x is 40. We have to find out the value of x from the numbers. Total numbers (36, 35, 34, 33, 32, and x) = 6 36 + 35 + 34 + 33 + 32 + x So, the average of the numbers = 6 numbers is 40] 170 + x = 40 6 170 + x = 40 6 x = 240-170 x = 70 = 40 [Since, the average of Therefore the value of x is 70. (9) Daughter-in-law According to the question, Aamir says, "Neha is the wife of the grandson of my mother". Or, we can say that the grandson of Aamir's mother is the son of Aamir. Or, we can say that Neha is the wife of Aamir's son. Therefore, we can say that Neha is the daughter-in-law of Aamir.
(10) ( 2-1)r ID : in-7-olympiad [10] According to the question, the radius of all the large circles is r. Let us assume rn as the radius of the inner smaller circle and connect the radius of all of the circles, as shown below. If we look at the figure carefully, we notice that AB = BC = 2r AC = 2r + 2rn Now, in right angle triangle ΔABC AC 2 = AB 2 + BC 2 AC 2 = (2r) 2 + (2r) 2 AC 2 = 4(r) 2 + 4(r) 2 AC 2 = 8(r) 2 AC = r 8 AC = r (2 2 2 AC = 2r 2 2r + 2rn = 2r 2 2rn = 2r 2-2r 2rn = 2r( 2-1) 2r( 2-1) rn = 2 rn = ( 2-1)r Thus, we can say that the radius of the inner smaller circle is ( 2-1)r.
(11) 360 ID : in-7-olympiad [11] If we look at the given figure carefully, we notice that it is a combination of triangle PRT and triangle QSU. Since, the sum of all the three angles of a triangle is 180. Therefore, P + R + T = 180, Q + S + U = 180 Hence, the sum of the angles P + Q + R + S + T + U = 180 + 180 = 360 (12) 6 If we observe the first and the second pattern, we notice the following relationship between the numbers: Middle number = ( Right number Top number ) + Left number First pattern: 14 = (4 3) + 2 Second pattern: 17 = (3 4) + 5 Let us assume that the missing number in the third pattern is x. Since, the third pattern should also follow the same relationship, Middle number = ( Right number Top number ) + Left number 41 = (7 5) + x x = 6 Thus, the missing number is 6.
(13) 70 ID : in-7-olympiad [12] If we look at the question carefully, we notice that lines AC and DE are parallel to each other and BAC = 35. BDE = BAC (Corresponding angles) BDE = 35 The sum of all the angles of a triangle is 180. In triangle BDE, BDE + BED + DBE = 180 35 + BED + 35 = 180 BED + 70 = 180 BED = 180-70 BED = 110 Line BC is a straight line and we know that the angles on one side of a straight line will always add to 180. Therefore, BED + DEC = 180 110 + x = 180 x = 180-110 x = 70 Therefore, the value of angle x is 70. (14) b. Two days before yesterday If two days after tomorrow will be Sunday, this means today is Thursday. If today is Thursday, this means two days before yesterday was Monday.
(15) b. D ID : in-7-olympiad [13] If we look at the regular polygon carefully, we notice that there are 5 sides of a regular polygon. 1 Therefore, the length of a side of the regular polygon = 5 Since, the distance walked by the dog on the periphery, in the clockwise direction = Therefore, the number of sides walked by the dog on the regular polygon = Distance walked by the dog 18 25 Length of a side of the polygon 18 = 25 1 5 = 18 25 5 1 = 18 5 = 3.6 It means that the dog walked on 3 sides of the regular polygon and the dog is walking on the 4 th side of the regular polygon, in the clockwise direction. Since, it started from point s, the dog will be on the side D, after walking periphery in the clockwise direction. Hence, option b is the correct answer. 18 25 distance on the