Question

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Answer 1

Answer:

1) 249

2) 1200

3) 8cm

4) 960

Step-by-step explanation:

1) The least no. that leaves 9 as reminder when divided by 10, 16, and 24 is 249 because,

249/10 ⇒ Q = 24, R = 98

249/16 ⇒ Q = 15, R = 9

249/24 ⇒ Q = 10, R = 9

Therefore the no. = 249

2) The smallest 4 digit no. exactly divisible by 24, 25, 60 is 1200

1200/24 ⇒ Q =  50, R = 0

1200/25 ⇒ Q =  48, R = 0

1200/60 ⇒ Q =  12, r = 0

Therefore the no. is 1200

3)The length of the string with which the sides can be measured exactly is 8cm.

Given,

L = 320mm = 32cm

b = 16cm

h = 8cm

By taking the HCF of the three sides is 8

By taking the length of the strength as 8cm the length of the box can be calculated by taking the measurement with the same string 4 times which is 8 × 4 = 32cm

By taking the length of the strength as 8cm the breadth of the box can be calculated by taking the measurement with the same string 2 times which

is 8 × 2 = 16cm

By taking the length of the strength as 8cm the height of the box can be calculated by taking the measurement with the same string 1 time which is 8 × 1 = 8cm

4)The greatest three digit no. divisible by the nos, 4, 5, and 6 is 960 because

960/4 ⇒ Q = 240, R = 0

960/5 ⇒ Q =  192, R = 0  

960/6 ⇒ Q =  160, R = 0

Therefore the no is 960