Real Numbers

 Q1   Find the greatest number of 5 digits exactly divisible by 12, 15 and 36.

Q2 Find the smallest number which when increased by 20 is exactly divisible by 90 and 144.

Q3  Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively.

Q4 If the HCF of 408 and 1032 is expressible in the form 1032p – 408 × 5 find p.

Q5  The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Q6 Find the least number of square tiles required to pave the ceiling of a room 15 m 17 cm long and 9m 2 cm broad

Q7 Three pieces of timber 42m,49m,63 m long have to be divided into planks of the same length.What is the greatest possible length of each plank

Case study questions

1. A seminar is being conducted by an educational organisation.The number of participants for Hindi,English and Maths are 60,84 and 108

1)In each room same number of participants are to be seated and all of them being in the same subject,maximum number of participants  that can be accomodated in each room is ???

2)Minimum number of rooms required for the event?

3)Product of HCF and LCM of 60 ,84 and 108 is??

Q9 Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

Q10 A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?

Q11 Find the smallest number which when increased by 17 is exactly divisible by 520 and 468

Q12 . A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What would be the greatest capacity of such a tin?

Q13 Find the smallest 4-digit number which is divisible by 18, 24 and 32.

Q14 The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Q15 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?

Q16 Find the LCM and HCF of the following :

(i) 25 × 54 × 72 × 136 and 23 × 56 × 7 × 173
(ii) a5 × b2 × c2 × d5 and a7 × b3 × e × f3 where a, b, c, d, e, and f are prime.