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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Question : Directions: If P denotes multiplication, Q denotes subtraction, S denotes addition and R denotes division, which of the following equations must be true?
Option 1: 7 S 56 P 2 R 28 = 11
Option 2: 36 R 6 P 2 S 4 = 19
Option 3: 64 R 8 P 3 S 6 = 72
Option 4: 36 R 9 S 4 P 2 = 14
Question : Directions: Select the option that represents the letters that, when placed from left to right in the blanks below, will complete the letter series. P _ R R _ P Q _ _ S _ Q R _ S P _ R R S
Option 1: R Q P Q R S Q
Option 2: S Q R R Q P R
Option 3: S Q Q R R P Q
Option 4: Q S R R P R Q
Question : If $ p(x+y)^{2}=5$ and $q(x-y)^{2}=3$, then the simplified value of $p^{2}(x+y)^{2}+4pq xy -q^{2}(x-y)^{2}$ is:
Option 1: $-(p+q)$
Option 2: $2(p+q)$
Option 3: $p+q$
Option 4: $-2(p+q)$
Question : Directions: If P denotes ×, Q denotes ÷, R denotes +, and S denotes –, then what will come into place of ? in the following equation? $\sqrt{256}$ P 3 S 66 Q 11 P 5 R 43 = ?
Option 1: 72
Option 2: 58
Option 3: 61
Option 4: 69
Question : If $3P=2Q$ and $2Q=3R$, then what is $P:Q:R$?
Option 1: $6:9:1$
Option 2: $2:3:2$
Option 3: $4:6:9$
Option 4: $4:6:1$
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