Question

Two numbers are in the ratio 21:17, if the HCF is 5.
Find the numbers.​

Answer 1

Step-by-step explanation:

21:17

and HCF =5

L.C.M=(21x,17x)

21×17×x

HCF=(21,17)=5

WE KNOW THAT,

LCM×HCF= PRODUCT OF NUMBER

5×21X×17X=21X×17X

X=5

21X=21×5=105

17X=17×5=85

THE NUMBER ARE =105 AND 85.

Answer 2

Given :–

• Two number are in ratio = 21:17.
• Highest common factor (H.C.F.) = 5.

To Find :–

• Two numbers.

Solution :–

Let,

The two numbers be 21x and 17x.

The least common multiple (L.C.M.) = 21x × 17x

The product of number = 21x × 17x

We know that,

L.C.M. × H.C.F. = Product of number.

⟹ (21x × 17x) × 5 = 21x × 17x

⟹ (357x) × 5 = 357x

⟹ $\dfrac{\cancel{357}x}{\cancel{357}x}$ = 5

⟹ 1x = 5

It means,

⟹ x = 5.

Now, we have to find both the numbers.

• 21x = 21 × 5 = 105
• 17x = 17 × 5 = 85

Check :–

Highest common factor (H.C.F.),

⟹ 105 = 5 × 3 × 7

⟹ 85 = 5 × 17

Since, 5 is the H.C.F. of 21:17.

So, the both the numbers 105 and 85 is correct.