A chemical processing plant uses two storage tanks, Tank X and Tank Y. Initially, the rati… — GRE General Test

A chemical processing plant uses two storage tanks, Tank $X$ and Tank $Y$ . Initially, the ratio of the volume of liquid in Tank $X$ to Tank $Y$ is $3 : 7$ . After $16\text{ liters}$ of liquid are transferred from Tank $Y$ to Tank $X$ , and an additional $8\text{ liters}$ of liquid are added to Tank $X$ from an external supply, the ratio of the volume of liquid in Tank $X$ to Tank $Y$ becomes $6 : 5$ . What was the original volume, in liters, of liquid in Tank $Y$ ?

A
24
B
49
56Cevap
D
80
E
96

Cevap

56 liters

By setting the initial volumes of Tank X and Tank Y to 3k and 7k respectively, the modified volumes after transfer and addition are (3k + 24) and (7k - 16). Setting their ratio equal to 6/5 yields 5(3k + 24) = 6(7k - 16), which simplifies to 27k = 216, or k = 8. Multiplying 8 by 7 gives the original volume of Tank Y as 56 liters.

Adım Adım Çözüm

Define initial quantities using a common ratio multiplier

k

Let the initial volume of Tank

X

3k

liters and the initial volume of Tank

Y

7k

liters.

The given initial ratio of

X : Y

3 : 7

Express the new volumes after the liquid transfers.

Tank

X

volume becomes

3k + 16 + 8 = 3k + 24

liters. Tank

Y

volume becomes

7k - 16

liters.

Transferring

16\text{ liters}

from Tank

Y

to Tank

X

decreases Tank

Y

16

and increases Tank

X

16

. Adding an extra

8\text{ liters}

to Tank

X

brings its total increase to

24\text{ liters}

Set up the proportion with the new ratio and solve for

k

\begin{aligned} \frac{3k + 24}{7k - 16} &= \frac{6}{5} \\[6pt] 5(3k + 24) &= 6(7k - 16) \\[6pt] 15k + 120 &= 42k - 96 \\[6pt] 216 &= 27k \\[6pt] k &= 8 \end{aligned}

The new ratio of Tank

X

to Tank

Y

is given as

6 : 5

Calculate the original volume of Tank

Y

Original volume of Tank

Y = 7k = 7 \times 8 = 56\text{ liters}

Tank

Y

initially contained

7k

liters.

Anahtar Kavram

Algebraic setup of part-to-part ratios undergoing quantitative adjustments

Tahmini Süre:1m 30s

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