Xth MATHEMATICS ASSIGNMENT 100424_001
CH.01 REAL NUMBERS
(Applications of HCF and LCM)
Q.1 Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? (excluding the one at start) [ ANS: LCM(2,4,6,8,10,12) = 120 sec= 2 min. , 15 times]
Q.2 The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8:20:00 hrs, when will they again change simultaneously ?
[ ANS: LCM= 432 seconds = 7 min 12 sec . Hence answer is 08:27:12 hrs]
Q.3 A merchant has 120 ltrs of and 180 ltrs of two kinds of oil. He wants the sell oil by filling the two kinds of oil in tins of equal volumes. What is the greatest of such a tin.
[ ANS: HCF =60 ltrs.]
Q.4 Find the least number of soldiers in a regiment such that they stand in rows of 15, 20, 25 and form a perfect square.
[ ANS: LCM = 300 & SOLDIERS REQUIRED = 900 ]
Q.5 Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. [ ANS: HCF=2, TILES=344,864 ]
Q.6 A wine seller had three types of wine. 403 liters of 1st kind, 434 liters of 2nd kind and 465 liters of 3rd kind. Find the least possible number of casks of equal size in which different types of wine can be filled without mixing.
[ ANS: HCF=31, CASKS=(403/31) + (434/31) + (465/31)= 13 + 14 + 15 = 42 ]
Q.7 The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed ?
[ Hint: let numbers are 49x and 49y then x + y =12, The possible pairs of values of (x, y) are (1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6) ]
Q.8 The product of two numbers is 2028 and their H.C.F. is 13. Find the number of such pairs .
[ Hint : Let two numbers are 13x and 13y then xy = 12, The possibles pairs of values of (x, y) are (1, 12), (2, 6), (3, 4) ]
Q.9 Lenin is preparing dinner plates. He has 12 pieces of chicken and 16 rolls. If he wants to make all the plates identical without any food left over, what is the greatest number of plates Lenin can prepare ?
[ ANS : HCF = 4]
Q.10 The drama club meets in the school auditorium every 2 days, and the choir meets there every 5 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium ?
[ANS : L.C.M of (2, 5) = 10 ]
Q.11 Lily has collected 8 Indian stamps and 12 international stamps. She wants to display them in identical groups of Indian and international stamps, with no stamps left over. What is the greatest number of groups Lily can display them in ?
[ Ans: HCF = 4 ]
Q.12 Abraham has two pieces of wire, one 6 feet long and the other 12 feet long. If he wants to cut them up to produce many pieces of wire that are all of the same length, with no wire left over, what is the greatest length, in feet, that he can make them ?
[ Ans : HCF = 06 feet ]
Q.13 Sarah is making friendship bracelets. She wants to make bracelets that are 8 inches long and 12 inches long. What is the smallest length of string she can use for each bracelet if she doesn’t want to have any leftover string? [ Ans : LCM = 24 ]
Q.14 Can two number can have HCF = 125 and LCM = 300 ? . Justify your answer
[ Ans : No, As HCF always divides LCM]
Q.15 Anish goes fishing every 5th day and Balaji goes fishing every 7th day. If Anish and Balaji both went fishing today, how many days until they will go fishing on the same day again? [ Ans: LCM = 35]
Q.16 Find the largest number which divides 245 and 1037, leavingr emainder 5 in each case. [ Ans: HCF(245-5,1037-5)=24
Q.17 Find the largest number which divides 129 and 545, leavingr emainders 3 and 5 respectively. [ Ans - HCF(129-3,545-5)=18]
Q.18 In a school there are two sections, namely A and B, of class X. There are 30 students in section A and 28 students in section B. Find the minimum number of books required for their class library so thatt hey can be distributed equally among students of section A or section B.
[ Ans : LCM=120]
Q.19 Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 respectively.
[ Ans: Required number = LCM (28,32) -20= 224-20 = 204 ]
20. Find the smallest number which when increased by 17 is exactlyd ivisible by both 468 and 520. [ Ans: LCM (468, 520) -17 = 4680-17 = 4663]
21.The HCF of two numbers is 23 and their LCM is 1449. If one of then umbers is 161, find the other. [ Ans: 207 ]
22. The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725,find the other. [ Ans: 435 ]
23. Check whether (15)^n ends with zero or not , where n is any integer [ Ans : No]
24. Explain why 8x7x4x11x5 - 11 is a composite number ?
25. Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.
[HINT : HCF always divides LCM completely.]
For other assignment on Ch 01 Real Numbers. Click below.
1.Assignment on " To prove given number is irrational"
2. Assignment on "Multiple choice questions" on Chapter real Numbers
3. Assignment on " Assertion Reasoning questions" on Chapter real Numbers
4. Assignment on " Case study questions" on Chapter real Numbers
5. 10th Maths Ch Real Numbers Question Bank
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