model 3 twice, thrice, one third etc. of numbers Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Let the third number be x,

∴ First number = 3x

∴ Second number = ${3x}/4$

According to the question,

3x + ${3x}/4$ + x = 3 × 95

⇒ ${12x+3x+4x}/4$ = 285

⇒ 19x = 285 × 4

⇒ x = ${285×4}/19$ = 60

Aliter : Using Rule 15,

From three numbers, first number is 'a’ times of 2nd number, 2nd number is 'b’ times of 3rd number and the average of all three numbers is x, then,

First number = $\text"3ab"/ \text"1+b+ab"$ x ; Second number = $\text"3b"/ \text"1+b+ab"$ x ; Third number = $\text"3b"/ \text"1+b+ab"$ x

Here, a = 4, b = $3/4$, x = 95

Third Number = $3/\text"1+b+ab"$ ×x

= $3/{1+{3/4}+4×{3/4}}$×95

= ${3×4}/{4+3+12}$×95 = 60

Answer: (d)

Let third number be x.

∴ Second number = 3x

and first number = ${3x}/2$

Now, x +3x+${3x}/2$=3×44

⇒ ${8x+3x}/2$=3×44

⇒ 11x = 6 × 44

⇒ x=${6×44}/11 = 24$

∴ The largest number = 3x = 3 × 24 = 72

Answer: (c)

Let the third number be x.

∴ The second number = 2x and the third number = 2 × 2x = 4x

According to the question, ${4x+2x+x}/3$ = 21

⇒ 7x = 21 × 3

⇒ x =${21×3}/7$ = 9

Aliter : Using Rule 15,

From three numbers, first number is 'a’ times of 2nd number, 2nd number is 'b’ times of 3rd number and the average of all three numbers is x, then,

First number = $\text"3ab"/ \text"1+b+ab"$ x ; Second number = $\text"3b"/ \text"1+b+ab"$ x ; Third number = $\text"3b"/ \text"1+b+ab"$ x

a = 2, b = 2, x = 21

First number = $\text"3ab"/ \text"1+b+ab"$x

= ${3×2×2}/{1+2+4}$×21

= $12/7$×21=36

Second number = $\text"3ab"/ \text"1+a+ab"$x = ${3×2}/7$×21 = 18

Third number = $3/ \text"1+a+ab"$x = $3/7$×21 = 9