ACT · Practice Sheet 20

1. 1.

   Quantitative Aptitude

   The marked price of an item is $1,800. After a 50% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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2. 2.

   Quantitative Aptitude

   Find the HCF and LCM of 8 and 22.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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3. 3.

   Physics

   An object starts at 13 m/s and accelerates at 7 m/s² for 12 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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4. 4.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 9 and common difference 4.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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5. 5.

   Quantitative Aptitude

   Two varieties costing $21 and $83 per kg are mixed to give a mixture worth $72 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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6. 6.

   Physics

   If 3,324 J of work is done in 33 s, find the power.

   Formula:Power

   $P = \dfrac{W}{t}$

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7. 7.

   Mathematics

   Find the slope of the line through (0, -7) and (6, -7).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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8. 8.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 7, find term number 26.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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9. 9.

   Quantitative Aptitude

   Two varieties costing $15 and $81 per kg are mixed to give a mixture worth $50 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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10. 10.

    Physics

    Find the force required to accelerate a 48 kg mass at 10 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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11. 11.

    Quantitative Aptitude

    A vehicle covers 93 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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12. 12.

    Quantitative Aptitude

    Find the average of these 6 numbers: 80, 86, 70, 51, 87, 39.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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13. 13.

    Quantitative Aptitude

    A invests $10,000 and B invests $10,000 for the same period. If the total profit is $8,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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14. 14.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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15. 15.

    Physics

    If 703 J of work is done in 44 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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16. 16.

    Physics

    A body moving at 10 m/s accelerates at 5 m/s² for 5 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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17. 17.

    Physics

    Find the force required to accelerate a 14 kg mass at 8 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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18. 18.

    Quantitative Aptitude

    A value changes from 600 to 720. Find the percentage increase.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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19. 19.

    Quantitative Aptitude

    The marked price of an item is $200. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

    View formula →
20. 20.

    Mathematics

    Find the distance between the points (-5, -8) and (1, -8).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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