Practice Finding with ratios - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Three numbers are in the ratio 2 : 3 : 4 and their H.C.F. is 12. The L.C.M. of the numbers is
(a)
(b)
(c)
(d)
Let the numbers be 2x, 3x and 4x respectively.
∴ HCF = x = 12
∴ Numbers are : 2 ×12 = 24
3 ×12 = 36, 4 ×12 = 48
LCM of 24, 36, 48
= 2 × 2 × 2 × 3 × 3 × 2 = 144
Q-2) Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is
(a)
(b)
(c)
(d)
Let the number be 3x and 4x.
Their LCM = 12x
According to the question,
12x = 240
⇒ x = $240/12$ = 20
∴ Smaller number = 3x = 3 × 20 = 60
Q-3) The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is
(a)
(b)
(c)
(d)
If the numbers be 2x and 3x,
then LCM = 6x
∴ 6x = 48 ⇒ x = 8
∴ Required sum = 2x + 3x = 5x
= 5 × 8 = 40
Q-4) Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is
(a)
(b)
(c)
(d)
Let the numbers be 3x and 4x.
∴ Their LCM = 12x
∴ 12x = 84
⇒ x = $84/12$ = 7
∴ Larger number = 4x = 4 × 7 = 28
Q-5) Two numbers are in the ratio 3 : 4. The product of their H.C.F. and L.C.M. is 2028. The sum of the numbers is
(a)
(b)
(c)
(d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the numbers be 3x and 4x respectively
First number × second number
= HCF × LCM
⇒ 3x × 4x = 2028
⇒ $x^2 = 2028/{3×4}$ = 169
∴ x = $√{169}$ = 13
∴ Sum of the numbers
= 3x + 4x = 7x = 7 × 13 = 91
Q-6) If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two numbers is
(a)
(b)
(c)
(d)
Let the two numbers are 2x and 3x respectively.
According to question,
LCM = 54
x (3×2)= 54
⇒ x = 9
Numbers = 2x = 2 × 9 = 18
and, 3x = 3 × 9 = 27
Sum of the two numbers
= 18 + 27 = 45
Q-7) The ratio of the sum to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller number is :
(a)
(b)
(c)
(d)
Let the numbers be 4x and 4y
where x and y are prime to each other.
LCM = 4xy
∴ $(\text"4x+4y")/ \text"4xy"$ = $7/12$
⇒ 12 (x + y) = 7 xy
⇒ x = 3, y = 4
∴ Smaller number = 4 × 3 = 12
Q-8) Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is
(a)
(b)
(c)
(d)
Numbers = 3x and 4x
HCF = x = 4
∴ LCM = 12x = 12 × 4 = 48
Q-9) The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is :
(a)
(b)
(c)
(d)
If the numbers be 3x and 4x,
then
HCF = x = 5
∴ Numbers = 15 and 20
∴ LCM = 60
Q-10) The H.C.F. and L.C.M. of two numbers are 21 and 84 respectively. If the ratio the two numbers is 1 : 4, then the larger of the two numbers is
(a)
(b)
(c)
(d)
HCF of numbers = 21
∴ Numbers = 21x and 21y
Where x and y are prime to each other.
Ratio of numbers = 1 : 4
∴ Larger number = 21 × 4 = 84