CSAT Solved Papers/ 2024/Q25

2024 CSAT — Q25

Quant Arithmetic & numeracy 2.5 marks Medium

Two persons $P$ and $Q$ enter into a business. $P$ puts $14{,}000$ rupees more than $Q$ , but $P$ has invested for $8$ months and $Q$ has invested for $10$ months. If $P$ ‘s share is $400$ rupees more than $Q$ ‘s share out of the total profit of $2{,}000$ rupees, what is the capital contributed by $P$ ?

A 30,000 rupees Answer
B 26,000 rupees
C 24,000 rupees
D 20,000 rupees

Worked rationale

Profit splits in the ratio of capital × time. First fix the share ratio: total profit $2000$ , and $P$ ‘s share exceeds $Q$ ‘s by $400$ , so

P\text{'s share} = 1200,\quad Q\text{'s share} = 800 \;\Rightarrow\; P:Q = 1200:800 = 3:2.

Let $Q$ ‘s capital be $c$ ; then $P$ ‘s capital is $c + 14000$ . Equate the profit ratio to the capital-time ratio:

\frac{(c+14000)\times 8}{c \times 10} = \frac{3}{2}.

Cross-multiply: $2 \cdot 8 (c+14000) = 3 \cdot 10\, c \Rightarrow 16c + 224000 = 30c \Rightarrow 14c = 224000 \Rightarrow c = 16000.$

So $P$ ‘s capital $= 16000 + 14000 = 30000$ .

Answer: (a) 30,000 rupees.

Why the other options miss

B

an arithmetic slip: solves for $Q$ ‘s capital-plus-something or mis-multiplies the $8$ and $10$ , landing one step off.
C

left time out of the weighting: splits profit by capital alone, ignoring the unequal $8$ - vs $10$ -month durations, so the ratio comes out wrong.
D

answered the wrong person: reports $Q$ ‘s figure or uses share ratio $1:1$ , missing the $400$ -rupee gap that fixes $3:2$ .

Specialist insight

Two ratios must be kept distinct: the share ratio (from the profit split, $1200:800=3:2$ ) and the weight ratio (capital $\times$ time). The single most common error is dividing profit by capital only — but $P$ invested for fewer months, so time must enter. Set up one linear equation equating the two ratios and solve for $Q$ ‘s capital, then add $14000$ . Reading “ $P$ ‘s share is $400$ more out of $2000$ ” as $1200$ vs $800$ (not as $400$ vs $1600$ ) is the other place marks leak.

The trap, in one line

Weight by capital $\times$ time (not capital alone): $P$ invested $8$ months vs $Q$ 's $10$ , and the share ratio is $1200:800=3:2$ — solving gives $P$ 's capital $=30{,}000$ .

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