M.7 2027 Practice Sets — 35 MCQs with Solutions

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30 practice MCQs built on the same rule types as 2022–2026, with new numbers. Attempt each on paper first, then open the solution. Aim for under 60 seconds per question.

Set A · Percentages

A1

Question: A shopkeeper sells 35% of his stock and has 1300 items left. How many items did he start with?

Options: (A) 1800 (B) 2000 (C) 2200 (D) 2500

✅ Answer: (B) 2000

$$\text{Original}=\frac{1300}{1-0.35}=\frac{1300}{0.65}=2000$$

A2

Question: A price rises by 20% and then falls by 20%. What is the net change?

Options: (A) 0% (B) −2% (C) −4% (D) +4%

✅ Answer: (C) −4%

$$1.20\times0.80=0.96\;\Rightarrow\;4\%\ \text{decrease}$$

A3

Question: Find $15\%$ of 80 plus $25\%$ of 60.

Options: (A) 25 (B) 27 (C) 30 (D) 35

✅ Answer: (B) 27

$$0.15\times80+0.25\times60=12+15=27$$

A4

Question: A salary of Rs. 40,000 is increased by 12.5%. New salary?

Options: (A) 44,000 (B) 45,000 (C) 46,000 (D) 48,000

✅ Answer: (B) 45,000

$$40000\times1.125=45000$$

A5

Question: 60% of a number is 90. What is 40% of the number?

Options: (A) 40 (B) 50 (C) 60 (D) 75

✅ Answer: (C) 60

$$N=\frac{90}{0.6}=150,\qquad 0.4\times150=60$$

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Set B · Ratio, proportion and mixtures

B1

Question: Rs. 1200 is shared in the ratio 3 : 5 : 2. What is the largest share?

Options: (A) 500 (B) 600 (C) 720 (D) 240

✅ Answer: (B) 600

$$\frac{5}{3+5+2}\times1200=\frac{5}{10}\times1200=600$$

B2

Question: Boys : girls = 7 : 5 and the total is 1440. How many girls?

Options: (A) 540 (B) 600 (C) 720 (D) 840

✅ Answer: (B) 600

$$\text{Girls}=\frac{5}{12}\times1440=600$$

B3

Question: What must be added to both terms of 5 : 9 to make the ratio 3 : 4?

Options: (A) 5 (B) 6 (C) 7 (D) 8

✅ Answer: (C) 7

$$\frac{5+x}{9+x}=\frac34\;\Rightarrow\;20+4x=27+3x\;\Rightarrow\;x=7$$

B4

Question: A 40 L mixture has milk : water = 3 : 1. How much water must be added to make the ratio 1 : 1?

Options: (A) 10 L (B) 15 L (C) 20 L (D) 30 L

✅ Answer: (C) 20 L

$$\text{Milk}=30,\ \text{Water}=10;\qquad 10+x=30\;\Rightarrow\;x=20$$

B5

Question: The ratio of the times taken by A and B is 4 : 5. If A takes 40 minutes, how long does B take?

Options: (A) 32 min (B) 45 min (C) 50 min (D) 60 min

✅ Answer: (C) 50 min

$$t_{B}=40\times\frac54=50$$

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Set C · Ages

C1

Question: A father is 4 times his son's age. In 5 years the sum of their ages is 50. Father's present age?

Options: (A) 28 (B) 30 (C) 32 (D) 36

✅ Answer: (C) 32

$$(4x+5)+(x+5)=50\;\Rightarrow\;5x=40\;\Rightarrow\;x=8,\ \text{father}=32$$

C2

Question: A mother is 3 times her daughter's age. In 10 years the sum of their ages is 76. Mother's present age?

Options: (A) 36 (B) 40 (C) 42 (D) 45

✅ Answer: (C) 42

$$(3x+10)+(x+10)=76\;\Rightarrow\;4x=56\;\Rightarrow\;x=14,\ \text{mother}=42$$

C3

Question: Ali is 3 times Bilal's age and their ages sum to 40. What will Ali's age be after 5 years?

Options: (A) 30 (B) 35 (C) 40 (D) 45

✅ Answer: (B) 35

$$3x+x=40\;\Rightarrow\;x=10,\ \text{Ali}=30\;\Rightarrow\;30+5=35$$

C4

Question: A is 6 years older than B. In 4 years A will be twice as old as B. B's present age?

Options: (A) 2 (B) 4 (C) 6 (D) 8

✅ Answer: (A) 2

$$(x+6)+4=2(x+4)\;\Rightarrow\;x+10=2x+8\;\Rightarrow\;x=2$$

C5

Question: A man is 4 times his son's age. In 6 years he will be 3 times his son's age. Son's present age?

Options: (A) 10 (B) 12 (C) 14 (D) 16

✅ Answer: (B) 12

$$4x+6=3(x+6)\;\Rightarrow\;4x+6=3x+18\;\Rightarrow\;x=12$$

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Set D · Work, speed and time

D1

Question: 12 men finish a job in 15 days. How many days will 18 men take?

Options: (A) 8 (B) 9 (C) 10 (D) 12

✅ Answer: (C) 10

$$D_{2}=\frac{12\times15}{18}=10$$

D2

Question: A can do a job in 10 days and B in 15 days. How long together?

Options: (A) 5 (B) 6 (C) 7.5 (D) 8

✅ Answer: (B) 6 days

$$\frac1T=\frac1{10}+\frac1{15}=\frac{3+2}{30}=\frac16$$

D3

Question: A 150 m train crosses a pole in 10 s. Speed in km/h?

Options: (A) 45 (B) 54 (C) 60 (D) 72

✅ Answer: (B) 54 km/h

$$v=\frac{150}{10}=15\ \text{m/s}=15\times\frac{18}{5}=54\ \text{km/h}$$

D4

Question: A 180 m train crosses a 270 m platform in 15 s. Speed in km/h?

Options: (A) 90 (B) 96 (C) 108 (D) 120

✅ Answer: (C) 108 km/h

$$v=\frac{180+270}{15}=30\ \text{m/s}=30\times\frac{18}{5}=108\ \text{km/h}$$

D5

Question: A car travels at 60 km/h for 2 hours and at 90 km/h for 1 hour. Average speed?

Options: (A) 65 (B) 70 (C) 75 (D) 80

✅ Answer: (B) 70 km/h

$$\bar{v}=\frac{60\times2+90\times1}{2+1}=\frac{210}{3}=70$$

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Set E · Exponents and algebra

E1

Question: Evaluate $25^{\frac12}\times25^{-\frac12}+25^{0}$.

Options: (A) 0 (B) 1 (C) 2 (D) 26

✅ Answer: (C) 2

$$25^{\frac12-\frac12}+1=25^{0}+1=1+1=2$$

E2

Question: Evaluate $8^{\frac23}$.

Options: (A) 2 (B) 4 (C) 16 (D) 64

✅ Answer: (B) 4

$$8^{\frac23}=\left(\sqrt[3]{8}\right)^{2}=2^{2}=4$$

E3

Question: What is the sum of the roots of $x^{2}-7x+12=0$?

Options: (A) −7 (B) 7 (C) 12 (D) −12

✅ Answer: (B) 7

$$(x-3)(x-4)=0\;\Rightarrow\;x_{1}+x_{2}=3+4=7=-\frac{b}{a}$$

E4

Question: If $a+b=7$ and $ab=10$, find $a^{2}+b^{2}$.

Options: (A) 29 (B) 39 (C) 49 (D) 59

✅ Answer: (A) 29

$$a^{2}+b^{2}=(a+b)^{2}-2ab=49-20=29$$

E5

Question: Solve $3x-5=2x+7$.

Options: (A) 2 (B) 7 (C) 12 (D) −12

✅ Answer: (C) 12

$$3x-2x=7+5\;\Rightarrow\;x=12$$

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Set F · Geometry, sets and series

F1

Question: A regular polygon has an exterior angle of $45^{\circ}$. How many sides?

Options: (A) 6 (B) 8 (C) 9 (D) 10

✅ Answer: (B) 8

$$n=\frac{360^{\circ}}{45^{\circ}}=8$$

F2

Question: A semicircle has radius 14 cm. Its perimeter (use $\pi=\frac{22}{7}$)?

Options: (A) 58 (B) 72 (C) 86 (D) 44

✅ Answer: (B) 72 cm

$$P=\pi r+2r=\frac{22}{7}\times14+28=44+28=72$$

F3

Question: Total surface area of a cylinder with $r=7$ cm, $h=10$ cm ($\pi=\frac{22}{7}$)?

Options: (A) 748 (B) 440 (C) 704 (D) 880

✅ Answer: (A) 748 cm²

$$2\pi r(r+h)=2\times\frac{22}{7}\times7\times17=44\times17=748$$

F4

Question: In a class of 50, 30 play cricket, 25 play football and 10 play both. How many play neither?

Options: (A) 0 (B) 5 (C) 10 (D) 15

✅ Answer: (B) 5

$$50-(30+25-10)=50-45=5$$

F5

Question: Find the next term: 3, 6, 12, 24, ?

Options: (A) 36 (B) 42 (C) 48 (D) 54

✅ Answer: (C) 48

$$\text{Each term}\times2\;\Rightarrow\;24\times2=48$$

F6 (bonus)

Question: Find the next term: 2, 5, 10, 17, 26, ?

Options: (A) 35 (B) 36 (C) 37 (D) 38

✅ Answer: (C) 37

$$\text{Differences }3,5,7,9\;\Rightarrow\;\text{next }11\;\Rightarrow\;26+11=37\quad(\text{terms }n^{2}+1)$$

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Set G · Your original 2027 predictions (kept from the earlier page)

G1

Question: Two workers' times are in the ratio 5 : 4. The first takes 100 minutes. How long does the second take?

✅ Answer: 80 minutes

$$t_{2}=100\times\frac{4}{5}=80\ \text{min}$$

Note: if instead the worker with part 4 takes 100 min, the other takes $100\times\frac54=125$ min — always identify which person the ratio part belongs to.

G2

Question: Evaluate $16^{\frac12}\times16^{-\frac12}-16^{0}$.

Options: (A) −1 (B) 0 (C) 1 (D) 2

✅ Answer: (B) 0

$$16^{\frac12-\frac12}-16^{0}=1-1=0$$

G3

Question: Find $n$ for a regular polygon with exterior angle $40^{\circ}$.

Options: (A) 8 (B) 9 (C) 10 (D) 12

✅ Answer: (B) 9 (nonagon)

$$n=\frac{360^{\circ}}{40^{\circ}}=9$$

G4

Question: In a survey of 150 people, 80 like tea, 70 like coffee and 30 like both. How many like neither?

Options: (A) 20 (B) 30 (C) 40 (D) 50

✅ Answer: (B) 30

$$150-(80+70-30)=150-120=30$$