44. If 4P = 5Q and 3Q = 4R, then what is the value of P: Q: R? A 7:6:2 B 10:8:3 C 5:4:3 D 25:16:10

General
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  1. If 4P = 5Q and 3Q = 4R, then what is the value of P: Q: R? A 7:6:2 B 10:8:3 C 5:4:3 D 25:16:10
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If 4P = 5Q and 3Q = 4R, then find the value of P: Q: R.

To find the values of (P:Q:R), we first need to express (P), (Q), and (R) in terms of a common variable. Let’s go through the equations step by step.

Step 1: Express (P) in Terms of (Q)

Given:
4P = 5Q

From this equation, solve for (P):
P = \frac{5Q}{4}

Step 2: Express (R) in Terms of (Q)

Also given:
3Q = 4R

From this equation, solve for (R):
R = \frac{3Q}{4}

Step 3: Express all in terms of (Q)

Now we have:
P = \frac{5Q}{4}
Q = Q
R = \frac{3Q}{4}

Step 4: Calculate the Ratios (P:Q:R)

Find a common denominator for the ratios. Since (P), (Q), and (R) are all expressed in terms of (Q), we’ll convert them to the same scale:

  • Multiply all terms by 4 to eliminate fractions and express ratios in the simplest form:
    • (P = \frac{5Q}{4} \times 4 = 5Q)
    • (Q = Q \times 4 = 4Q)
    • (R = \frac{3Q}{4} \times 4 = 3Q)

So:
P:Q:R = 5Q:4Q:3Q

Divide each by (Q) (since ratios are scale-invariant):
P:Q:R = 5:4:3

Conclusion

The value of (P:Q:R) is 5:4:3. Thus, the correct answer is option C.

@anonymous12