Question : If p : q = 4 : 5, q : r = 3 : 4 and r : s = 2 : 5, then p : s is:
Option 1: 2 : 5
Option 2: 6 : 25
Option 3: 5 : 2
Option 4: 25 : 6
Correct Answer: 6 : 25
Solution :
Here, we have,
$\frac{p}{q} =\frac{4}{5}, \frac{q}{r} =\frac{3}{4}, \frac{r}{s} = \frac{2}{5}$
Now first, take
$\frac{p}{q} =\frac{4}{5}$ and $\frac{q}{r} =\frac{3}{4}$
As q is common in both. So, it should be equal for both
Multiply $\frac{p}{q}$ by 3 and $\frac{q}{r}$ by 5
$So,\frac{p}{q} =\frac{4×3}{5×3}$ and $\frac{q}{r}=\frac{3×5}{4×5}$
$\frac{p}{q} =\frac{12}{15}$, $\frac{q}{r}=\frac{15}{20}$
Now, $\frac{q}{r}=\frac{15}{20}$ and $\frac{r}{s} =\frac{2}{5}$
As r is common in both. So, multiply by 10 in $\frac{r}{s}$ to make r equal in both
⇒ $\frac{q}{r}=\frac{15}{20}, \frac{r}{s}=\frac{2×10}{5×10} = \frac{20}{50}$
Now, the new ratio of $\frac{p}{q}=\frac{12}{15}$, $\frac{q}{r}=\frac{15}{20}$, $\frac{r}{s}=\frac{20}{50}$
Now, p : q : r : s = 12 : 15 : 20 : 50
⇒ p : s = 12 : 50 = 6 : 25
Thus, the ratio of p : s is 6 : 25.
Hence, the correct answer is 6 : 25.
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