Q: Find the Greatest Number that will devide 43, 91 and 183 so as to leave the same remainder in each case
Solution: Required Number = H.C.F of (91- 43), (183- 91) and (183-43)
= H.C.F of 48, 92, and 140 = 4Q: In a palace, three different types of coins are there namely gold, silver and bronze. The number of gold, silver and bronze coins is 18000, 9600 and 3600 respectively. Find the minimum number of rooms required if in each room should give the same number of coins of the same type ?
Solution: Gold coins = 18000 , Silver coins = 9600 , Bronze coins = 3600 Find a number which exactly divide all these numbers That is HCF of 18000, 9600& 3600 All the value has 00 at end so the factor will also have 00. HCF for 180, 96 & 36. Factors of 180 = 3 x 3 x 5 x 2 x 2 96 = 2 x 2 x 2 x 2 x 2 x 3 36 = 2 x 2 x 3 x 3 Common factors are 2x2×3=12 Therefore, Actual HCF is 1200 Gold Coins 18000/1200 will be in 15 rooms Silver Coins 9600/1200 will be in 8 rooms Bronze Coins 3600/1200 will be in 3 rooms Total rooms will be (15+8+3) = 26 rooms.
Q: A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Solution: Let us calculate both the length and width of the room in centimeters. Length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room. Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48 Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117
Q: If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ?
Solution: SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (15)(15)/100 % = 2.25%
Q: Anil purchases two books for Rs.100. He sells first at loss of 5% and second al 20% profit. If he gets Overall profit of 5% then what is cost of first book?
Solution: -5-----------------------5-------------------20 5-(-5) = 10 20-5= 15 Ratio of cost price of book1 and book2 = 3:2 Then cost price of book 1 is given by (3/5) x 100 = Rs. 60.
Q: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
Solution: Since the month begins with a Sunday, so there will be five Sundays in the month, Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285.
Q: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday ?
Solution: M + Tu + W + Th = 4 x 48 = 192Tu + W + Th + F = 4 x 46 = 184M = 42Tu + W + Th = 192 - 42 = 150F = 184 – 150 = 34
Q: A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
Solution: let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160
Q: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Solution: Let the third number be x. Then, first number = 120% of x =120x/100 = 6x/5 Second number =150% of x = 150x/100 = 3x/2 Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5
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