Question : The ratio of incomes of $\mathrm{P}$ and $\mathrm{Q}$ is $1: 2$. Ratio of income of $\mathrm{Q}$ and $\mathrm{R}$ is $3: 2$. If one-third of $\mathrm{P}$ 's income is INR 4400 less than half of P's income, then what is Q's income?
Option 1: INR 56600
Option 2: INR 52800
Option 3: INR 46600
Option 4: INR 41200
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Correct Answer: INR 52800
Solution : Given: The ratio of incomes of P and Q is 1: 2 The ratio of income of Q and R is 3: 2 P's income = $x$ Q's income = $2x $ According to the given information: One-third of P's income is INR 4400 less than half of P's income. ⇒ $(\frac{1}{3})x = (\frac{1}{2})× x - 4400$ ⇒ $2x = 3x - 26400$ ⇒ $3x – 2x = 26400$ ⇒ $x = 26400$ So Q's income = $2x$ = 2 × 26400 = INR 52800 Hence, the correct answer is INR 52800.
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Question : P's income is 250 percent of Q's income and P's expenditure is 180 percent of Q's expenditure. If P's income is 400 percent of Q's expenditure, then what is the respective ratio of P's savings and Q's savings?
Option 1: 11 : 5
Option 2: 5 : 2
Option 3: 11 : 3
Option 4: 8 : 3
Question : P's income is 150% of Q's income and P's expenditure is 60% of Q's expenditure. If Q saves 20% of his income, then how much percentage does P save of his own income?
Option 1: 68%
Option 2: 60%
Option 3: 72%
Option 4: 75%
Question : An amount of Rs.12,029 is divided among P, Q, and R such that P's share is 5 times Q's share and R's share is one-third of P's share. what is the share of R?
Option 1: Rs. 2,718
Option 2: Rs. 2,312
Option 3: Rs. 2,615
Option 4: Rs. 2,518
Question : If $\sin \theta+\tan \theta=\mathrm{p}$ and $\tan \theta-\sin \theta=\mathrm{q}$, then which of the relation satisfies for given values of $\mathrm{p}$ and $\mathrm{q}$?
Option 1: $\mathrm{p}^2-\mathrm{q}^2=4 \sqrt{\mathrm{pq}}$
Option 2: $\mathrm{p}^2-\mathrm{q}^2=8 \sqrt{\mathrm{pq}}$
Option 3: $\mathrm{p}^2+\mathrm{q}^2=4 \sqrt{\mathrm{pq}}$
Option 4: $\mathrm{p}^2+\mathrm{q}^2=4 \mathrm{pq}$
Question : Directions: There are five friends I, J, K, L, and M. K's income is more than L's income but less than M's income. J's income is the least. I's income is less than K's income. Whose income is the maximum?
Option 1: L
Option 2: I
Option 3: K
Option 4: M
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