Mathematics

If the price falls by 10%, the new price is 90% of the original. To keep expenditure the same, consumption must increase so that (new consumption) × (new price) = original expenditure. Let the increase be x%, then (1 + x/100) × 90% = 100%, solving gives x = 11 1/9%.

The relative speed of the faster train with respect to the slower train is (60 - 40) = 20 km/h, which is 20 × (1000/3600) = 5.56 m/s. The total length to be covered to pass the slower train is 140 + 120 = 260 meters. Time taken = distance / speed = 260 / 5.56 ≈ 46.8 seconds = 0.78 minutes. However, since the question asks for the time for the faster train to pass the slower one, the correct calculation is 260 / 16.67 (relative speed in m/s) which is incorrect here. Recalculating: 20 km/h = 5.56 m/s, so time = 260 / 5.56 ≈ 46.8 seconds = 0.78 minutes. The original answer C (0.78 minutes) is correct, so the initial selection was correct. Therefore, correct_answer is C.

The price after a 24% decrease is Rs.912, which means Rs.912 is 76% of the original price (100% - 24% = 76%). To find the original price, divide 912 by 0.76: 912 ÷ 0.76 = 1200. Therefore, the original cost of the article is Rs.1200, which corresponds to option C.

The relative speed between the two boys is 5.5 kmph - 5 kmph = 0.5 kmph. To be 8.5 km apart, time = distance / relative speed = 8.5 / 0.5 = 17 hours. However, since the options include 17 hr as A and 14 hr as B, and the calculation shows 17 hr, the correct answer is A, not B. Therefore, the correct answer is A.

Let the number be x. The problem states that when the number is multiplied by 15, the result increases by 196 compared to the original number. This can be expressed as 15x = x + 196. Simplifying, 15x - x = 196, which gives 14x = 196. Dividing both sides by 14, we get x = 14. Therefore, the correct answer is 14 (option A).

Let the number of boys be 11x and girls be 13x. After 4 boys and 8 girls join, the ratio becomes (11x + 4) : (13x + 8) = 4 : 5. Solving this gives x = 8. The total strength is 11x + 13x = 24x = 192. However, this contradicts the options, so rechecking: (11x + 4)/(13x + 8) = 4/5 leads to 5(11x + 4) = 4(13x + 8) => 55x + 20 = 52x + 32 => 3x = 12 => x = 4. Total strength = 24x = 96, which matches option A.

The downstream speed is 50 km / 5 hr = 10 km/hr, and the upstream speed is 24 km / 6 hr = 4 km/hr. Let the boat speed be b and the river speed be r. Then, b + r = 10 and b - r = 4. Solving these gives b = 7 km/hr and r = 3 km/hr, matching option A.

Let the three numbers be 3x, 4x, and 6x. Their product is (3x)(4x)(6x) = 72x^3 = 1944. Solving for x^3 gives x^3 = 27, so x = 3. The largest number is 6x = 18.

Let Khadija's current age be x. After one year, her age will be x + 1. Ten years ago, her age was x - 10. The problem states that after one year, she will be twice as old as she was ten years ago, which translates to the equation: x + 1 = 2(x - 10). Solving this: x + 1 = 2x - 20 => 1 + 20 = 2x - x => x = 21. Therefore, Khadija's current age is 21, which corresponds to option C.

The equation $\frac{2x}{25}=\frac{6}{x/3}$ can be rewritten as $\frac{2x}{25}=\frac{6}{x/3}=\frac{18}{x}$ because dividing by $x/3$ is the same as multiplying by $3/x$. Cross-multiplying gives $2x\times x=25\times 18$, which simplifies to $2x^2=450$. Dividing both sides by 2 yields $x^2=225$, so $x=15$ or $x=-15$. Since only positive options are given, the correct answer is 15, which corresponds to option B.