M.3 MPT 2023 (Special) — Questions and Worked Solutions — Quantitative / Math

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Source: FPSC MPT 2023 (Special) — official key published. Where the numbers in the earlier extraction do not reproduce the key, a ⚠️ line shows the working and the likely wording difference.

Q1 · Standard form and thickness

Question: Thickness of 400 sheets, each $5\times10^{-2}$ mm?

✅ Official answer: 200 mm

Solution (numbers as extracted):

400\times5\times10^{-2}=400\times0.05=20\ \text{mm}

Concept: total thickness = number of sheets × thickness of one.

⚠️ 200 mm fits 4000 sheets ( $4000\times0.05=200$ ) or 0.5 mm per sheet. Check the printed numbers.

Q2 · Ratio of times

Question: Saba : Nida time ratio is 6 : 5. Saba takes 90 min. Nida takes?

✅ Answer: 75 min

Solution:

\frac{S}{N}=\frac65\;\Rightarrow\;N=90\times\frac56=75

Q3 · Odd one out

Question: Odd one out in 10, 25, 45, 54, 60, 75, 85.

✅ Answer: 54

Reason: every other number is a multiple of 5; $54$ is not.

Q4 · Standard form

Question: Write $0.0000738$ in standard form.

✅ Answer: $7.38\times10^{-5}$

Solution:

0.0000738=7.38\times10^{-5}\quad(\text{point moved 5 places right})

Q5 · Equilateral triangle

Question: Perimeter 24 cm; one side?

✅ Answer: 8 cm

Solution:

3s=24\;\Rightarrow\;s=8

Q6 · Percentage remaining

Question: A watchmaker sold 40% of his watches; 420 are left. Original number?

✅ Answer: 700

Solution:

x(1-0.40)=420\;\Rightarrow\;x=\frac{420}{0.6}=700

Q7 · Ages (Ali : Babar)

Question: Ages ratio problem; Babar's present age?

✅ Official answer: 20

Method: let the ratio give $A=ax,\ B=bx$ , then use the second condition (years ago / hence) to form one equation in $x$ .

🔎 The extraction does not carry the full statement, so only the method is shown.

Q8 · Simple interest from two amounts

Question: Rs. 815 in a given time and Rs. 854 one year later. Find the sum.

✅ Official answer: 737

Solution (2 years and 3 years):

\begin{aligned} SI_{\text{1 yr}}&=854-815=39\\ P&=815-2\times39=737 \end{aligned}

⚠️ The extraction lists 3 and 4 years, which would give $P=815-3\times39=698$ . The official 737 matches 2 and 3 years.

Q9 · Linear equation in words

Question: A number is doubled and 9 is added; the result is then trebled and equals 75. Find the number.

✅ Answer: 8

Solution:

3(2x+9)=75\;\Rightarrow\;2x+9=25\;\Rightarrow\;x=8

Q10 · Two integers

Question: The difference of two integers is 36 and the smaller is 60% of the larger. Find the value asked.

✅ Official answer: 54

Solution:

\begin{aligned} L-0.6L&=36\\ 0.4L&=36\\ L&=90,\quad \text{smaller}=0.6\times90=54 \end{aligned}

⚠️ 54 is the smaller integer; the sum would be 144. Check what the question asks.

Q11 · Average of evenly spaced values

Question: Five children born at equal gaps; average age 18; youngest?

✅ Official answer: 12

Solution for a gap of $g$ years (ages $x,\ x+g,\ldots,x+4g$ ):

\bar{x}=x+2g=18

With $g=3$ : $x=12$ (matches the key).
With $g=2$ : $x=14$ .

⚠️ The extraction says 2 years apart, but the key 12 corresponds to a 3-year gap.

Q12 · Mixture (apple : orange juice)

Question: Mixture ratio problem; how much more is needed?

✅ Official answer: 1000 ml

Method: let the mixture contain $a$ ml apple and $o$ ml orange; write the target ratio as $\frac{a+x}{o}=\frac{m}{n}$ (adding the missing juice) and solve for $x$ .

🔎 Full numbers are not in the extraction.