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Pair of Linear Equations in Two Variables
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10

Question:

[Section D]

A motor boat whose speed is $18$ km/h in still water takes $1$ hour more to go $24$ km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

Two water taps together can fill a tank in $9\dfrac{3}{8}$ hours. The tap of larger diameter takes $10$ hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Step-by-Step Solution

Key Concept: Main: $24/(18-x) - 24/(18+x) = 1$. OR: $1/x + 1/(x-10) = 8/75$.
[Main Question Solution]

$24/(18-x) - 24/(18+x) = 1 \Rightarrow x^2 + 48x - 324 = 0 \Rightarrow (x+54)(x-6) = 0 \Rightarrow x = 6$ km/h. [5.0 Marks]


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[OR Choice Question Solution]

$1/x + 1/(x-10) = 8/75 \Rightarrow 4x^2 - 115x + 375 = 0 \Rightarrow x = 25$ hours. Larger tap $= 15$ hours. [5.0 Marks]

Correct Answer: Main: 6 km/h | OR: Larger tap = 15 hrs, Smaller tap = 25 hrs
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