Question

13. The average of three number is 42. The first is twice
the second and the second is twice the third. The
difference between the largest and the smallest
number is
1) 18
2) 36
3) 5.4
4) 72​

Answer 1

GiveN:-

The average of three number is 42. The first is twice the second and the second is twice the third.

To FinD:-

The difference between the largest and the smallest number.

SolutioN:-

• Let the third no be x.
• Let the second number be 2x.
• Let the first no be 4x.
• Average = 42.

According to the question,

$\large\implies{\sf{x+2x+4x=42}}$

$\large\implies{\sf{7x=42}}$

$\large\implies{\sf{x=\dfrac{42}{7}}}$

$\large\implies{\sf{x=\dfrac{\cancel{42}}{\cancel{7}}}}$

$\large\therefore\boxed{\bf{x=6.}}$

The numbers are:-

1. First number = 4x = 4 × 6 = 24
2. Second number = 2x = 2 × 6 = 12
3. Third number = x = 6

VerificatioN:-

$\large\implies{\sf{24+12+6=42}}$

$\large\implies{\sf{42=42}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified.

Now the difference:-

• Largest number = 24
• Smallest number = 6

$\large\implies{\sf{Difference=Largest\:number-smallest\:number}}$

$\large\implies{\sf{Difference=24-6}}$

$\large\therefore\boxed{\bf{Difference=18.}}$

Difference between the largest and the smallest number is 18.

So, your answer is (1).