Question

There are 3 groups of people, A, B, and C. The total wages of 6 people from A, 5 from group B, and 14 from group C is $\$$660. The wages of the 6 people from A are equal to that of the 10 people from B. Also, the wages of the 5 people from B are equal to that of the 10 people from C. Find the total wages of 20 people from group A, 15 from group B, and 20 from group C.

• A. $1,890
• B. $2,000
• C. $1,900
• D. $1,325

Answer 1

The correct option is C $1,900

Let the daily wages of a person from group A, group B, and group C be X, Y, and Z, respectively.

Given:

The wages of 6 people from group A are equal to the wages of 8 people from group B.
$⟹6X=8Y$
$⟹X=\frac{8}{6}Y=\frac{4}{3}Y$ ----(1)

The wages of 5 people from group C are equal to the wages of 8 people from group C.
$⟹5Y=8Z$
$⟹Z=\frac{5}{10}Y=\frac{1}{2}Y$ ----(2)

It is also given that the wages of the 6 people from group A, 5 people from group B, and 14 people from group C is $\$$660.
$⟹6X+5Y+14Z=660$

Substituting the values of 'X' and 'Z', we get:
$⟹6\times \frac{5}{3}Y+5Y+14\times \frac{1}{2}Y=660$

$⟹10Y+5Y+7Y=660$

$⟹22Y=660$

$⟹Y=30$

The daily wage of a person from group B is $\$$30.

$X=\frac{5}{3}\times 30=50$ from (1)

$Z=\frac{1}{2}\times 30=15$ from (2)

The daily wage of a person from group A and group C is $\$$50 and $\$$15, respectively.

The wages of 20 people from A, 15 people from group B, and 20 from group C =
$⟹20\times 50+15\times 30+20\times 15$

$⟹1000+600+300$

$⟹1,900$

Therefore, the wages of 20 people from group A, 15 people from group B, and 20 people from group C are $\$$1,900.