ACT · Practice Sheet 16

1. 1.

   Quantitative Aptitude

   A can finish a job in 18 days and B in 11 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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2. 2.

   Quantitative Aptitude

   Find the compound interest on $4,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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3. 3.

   Physics

   Find the electrical power when 234 V drives a current of 17 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Physics

   Find the density of an object with mass 479 g and volume 12 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 10, find term number 6.

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 8 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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7. 7.

   Quantitative Aptitude

   Divide $705 between two people in the ratio 3:2. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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8. 8.

   Physics

   Find the momentum of a 8 kg body moving at 26 m/s.

   Formula:Linear Momentum

   $p = mv$

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9. 9.

   Physics

   A body moving at 15 m/s accelerates at 4 m/s² for 10 s. Find the distance travelled.

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

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

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10. 10.

    Quantitative Aptitude

    A vehicle covers 172 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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11. 11.

    Quantitative Aptitude

    Two varieties costing $23 and $93 per kg are mixed to give a mixture worth $82 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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12. 12.

    Quantitative Aptitude

    A invests $8,000 and B invests $2,000 for the same period. If the total profit is $27,000, find A's share.

    Formula:Partnership (profit share)

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

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13. 13.

    Physics

    Find the density of an object with mass 191 g and volume 24 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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14. 14.

    Physics

    A projectile is launched at 21 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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15. 15.

    Physics

    Find the density of an object with mass 279 g and volume 45 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    Mathematics

    Find term number 3 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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17. 17.

    Physics

    A body moving at 2 m/s accelerates at 4 m/s² for 3 s. Find the distance travelled.

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

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

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18. 18.

    Physics

    Find the density of an object with mass 131 g and volume 50 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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19. 19.

    Mathematics

    Find the slope of the line through (6, 1) and (1, 7).

    Formula:Slope of a Line

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

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20. 20.

    Physics

    A constant force of 13 N moves an object 41 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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