Q: Three cats are roaming in a zoo n such a way that when cat A takes 5 steps, B takes 6 steps and C takes 7 steps.But the 6 steps of A are equal to the 7 steps of B and 8 steps of C. what is the ratio of their speeds?
Solution: Frequency of step of A:B:C = 5 : 6 : 7 But in terms of size of step, 6A = 7B = 8C Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147
Q: A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
Solution: If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.
Q: The ratio of two numbers is 3 : 4 and their H.C.F is 4. Their L.C.M is
Solution: Let the numbers be 3x and 4x . Then their H.C.F = x. So, x=4 Therefore, The numbers are 12 and 16 L.C.M of 12 and 16 = 48
Q: The minimum value of LCM of given numbers is ........... the product of all the given numbers.
Solution: None
Q: The LCM and HCF of two numbers are 4284 and 32, respectively. If one of the numbers is 672, then the second number is;
Solution: 204
Q: HCF and LCM of two numbers are 11 and 825 respectively. If one number is 275 find the other number.
Solution: 33
Q: Three friends J, K and L jog around a circular stadium and complete one round in 12, 18 and 20 seconds respectively. In how many minutes will all the three meet again at the starting point.
Solution: All the three friends will meet at the starting point again after X seconds, such that X is the LCM of the times taken by J, K and L to complete one round. => LCM of 12, 18 and 20 = 180 seconds = 3 minutes. Hence 3 minutes is the answer.
Q: If the product of two numbers is 4941 and their LCM is 81, then their HCF is :
Solution: 61
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