Question

Find the difference between the largest share and the smaller share in each of the following ratios when $160 is shared among three people

A) 1:6:9

B) 2:5:13

C) 22:5:13

D) 32:11:37

Answer 1

Answer:

A.) 1:6:9-

Total Amount(in$) →160

Ratio of the amount shared →1:6:9

Let the share between all three people be x, 6x and 9x respectively.

→x + 6x + 9x = 160

→16x = 160 {Transposing 16 to RHS.}

→x = 160/16

→x = 10

Largest Share → 9x → 9×10 → 90$

Smallest Share → x → 10$

Difference between Largest and Smallest Share → 90$ - 10$

→ 80$

Hence, Difference between Largest and Smallest Share is 80$.

B.) 2:5:13-

Total Amount(in$) → 160

Ratio of the Shared amount→ 2:5:13

Let the amount to be shared be 2x, 5x and 13x respectively.

→ 2x + 5x + 13x = 160

→ 20x = 160 {Transposing 20x to RHS.}

→ x = 160/20

→ x = 8

Largest Share→ 13x → 13×8 → 104$

Smallest Share→ 2x → 2×8 → 16$

Difference between Largest and Smallest Share→ 104-16

→ 88$

Hence, Different between Largest and Smallest Share is $88.

C.) 22:5:13-

Total amount(in$)→ 160

Ratio of the Shared amount→ 22:5:13

Let the amount to be shared be 22x, 5x and 13x respectively.

→ 22x + 5x + 13x = 160x

→ 40x = 160x {Transposing 40x to RHS.}

→ x = 160/40

→ x = 4

Largest Share→ 22x → 22×4 → 88$

Smallest Share→ 5x → 5×4 → 20$

Difference between Largest and Smallest Share→ 88-20

→ 68$

Hence, Difference between Largest and Smallest Share is 68$.

D.) 32:11:37-

Total amount(in$) → 160$

Ratio of the Shared amount→ 32:11:37

Let the amount to be shared be 32x, 11x and 37x respectively.

→ 32x + 11x + 37x = 160x

→ 80x = 160x {Transposing 80x to RHS.}

→ x = 160/80

→ x = 2

Largest Share→ 37x → 37×2 → 74$

Smallest Share→ 11x → 11×2 → 22$

Difference between Largest and Smallest Share→ 74-22

→ 52$

Hence, Difference between Largest and Smallest Share is 52$.

[Hope it'll be helpful...]