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ACT · Practice Sheet 34

Sheet code: ACT-S34 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
An item is bought for $800 and sold for $1,200. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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2.
Quantitative Aptitude
The sum of the ages of two people is 40 years, and one is 18 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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3.
Physics
Find the force required to accelerate a 15 kg mass at 16 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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4.
Quantitative Aptitude
The marked price of an item is $1,400. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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5.
Quantitative Aptitude
Find the simple interest on $4,000 at 12% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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6.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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7.
Mathematics
Find the sum of the first 20 terms of an AP with first term 13 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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8.
Quantitative Aptitude
The sum of the ages of two people is 51 years, and one is 13 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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9.
Mathematics
Find the sum of the first 6 terms of an AP with first term 12 and common difference 3.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
Find the compound interest on $13,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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11.
Quantitative Aptitude
Find the HCF and LCM of 19 and 21.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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12.
Mathematics
Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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13.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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14.
Mathematics
Evaluate ∫ from 0 to 3 of 2x^3 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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15.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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16.
Physics
If 981 J of work is done in 50 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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17.
Quantitative Aptitude
A value changes from 800 to 400. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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18.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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19.
Quantitative Aptitude
A vehicle covers 200 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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20.
Mathematics
Find the distance between the points (-5, 5) and (8, -6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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