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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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)

Explanation:

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