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91. The product of two numbers is 396 × 576 and their LCM is 6336. Find their HCF = ?
(a × b) = (HCF and LCM)
396 × 576 = HCF × 6336
HCF = 36
Solution:
We, know that(a × b) = (HCF and LCM)
396 × 576 = HCF × 6336
HCF = 36
92. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35 is ?
4 × 5 × 7 × 8 = 1120
LCM = (20, 28, 32, 35) = 1120
∴ 1120 divided by 20, 28, 32, 35 completely
∴ Let x be subtracted from 5834
∴ 5834 - x = 1120
⇒ x = 5834 - 1120 = 4714
Solution:
LCM of (20, 28, 32, 35)4 × 5 × 7 × 8 = 1120
LCM = (20, 28, 32, 35) = 1120
∴ 1120 divided by 20, 28, 32, 35 completely
∴ Let x be subtracted from 5834
∴ 5834 - x = 1120
⇒ x = 5834 - 1120 = 4714
93. 21 mango trees, 42 apple trees and 56 orange trees have to be planted in rows such that each row contains the same numbers of trees of one variety only. Minimum number of row in which the trees may be planted is = ?
Number of trees in each row = HCF of 21, 42, 56 = 7
Hence number of rows
Solution:
For the minimum number of rows, the numbers of trees in each row must be the maximum.Number of trees in each row = HCF of 21, 42, 56 = 7
Hence number of rows
94. The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95cm is = ?
Solution:
Required length = HCF of 700cm, 385cm and 1295cm = 35cm
95. Two numbers are in the ratio 3:4. Their LCM is 84. The greater number is ?
LCM = 84 (given)
∴ LCM number = common factor (other factors)
x × 3 × 4 = 12x
⇒ 12x = 84
⇒ x = 7
∴ Number are = 3x = 7 × 3 = 21
4x = 7 × 4 = 28
greater number is 28
Solution:
Let numbers are = 3x & 4x respectivelyLCM = 84 (given)
∴ LCM number = common factor (other factors)
x × 3 × 4 = 12x
⇒ 12x = 84
⇒ x = 7
∴ Number are = 3x = 7 × 3 = 21
4x = 7 × 4 = 28
greater number is 28
96. The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pair is = ?
Let numbers are 12x and 12y respectively
LCM ⇒ 12xy = 924(given)
⇒ xy = 77
⇒ Possible pairs are
= (1 × 77) (7 × 11)
∴ Only two pairs are possible
Solution:
HCF = 12Let numbers are 12x and 12y respectively
LCM ⇒ 12xy = 924(given)
⇒ xy = 77
⇒ Possible pairs are
= (1 × 77) (7 × 11)
∴ Only two pairs are possible
97. The LCM of two numbers is 520 and their HCF is 4. If one of the numbers is 52, then the other number is = ?
HCF = 4
one number = 52
Let other number is y
52y = 4 × 520
⇒ y = 40
Solution:
LCM = 520HCF = 4
one number = 52
Let other number is y
52y = 4 × 520
⇒ y = 40
98. The capacity of two pots is 120 litres and 56 litres respectively. Find the capacity of a container which can exactly measure the contents of the two pots = ?
= 8 litres = 8000 cc [∴ 1 litres = 1000 cc]
Solution:
Required capacity = HCF of 120 litres and 56 litres= 8 litres = 8000 cc [∴ 1 litres = 1000 cc]
99. A daily wage labourer was engaged for a certain number of days for Rs. 5750, but being absent on some of those days he was paid only Rs. 5000. What was his maximum possible daily wage ?
Because of his being absent he was paid Rs. 750 less.
Now check with option.
Since maximum possible daily wages is asked so it will be Rs. 250
OR :
Maximum possible daily wage
= HCF of Rs. 5750 and Rs. 5000
= Rs. 250
Solution:
Try to solve these kind of question by optionBecause of his being absent he was paid Rs. 750 less.
Now check with option.
Since maximum possible daily wages is asked so it will be Rs. 250
OR :
Maximum possible daily wage
= HCF of Rs. 5750 and Rs. 5000
= Rs. 250
100. The product of two numbers is 2028 and their HCF is 13. The number of such of pair is = ?
Let number are 13x & 13y respectively
Only two pair are possible
Solution:
HCF = 13 (given)Let number are 13x & 13y respectively
Only two pair are possible
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