Q&A: practice questions with answers

Concept: Solve brackets from inside out, then multiply.

1. $(7-6)$ gives 1.
2. $\frac{14}{7}=2$ and $\frac{19}{1}\times 1=19$, so the second bracket = 21.
3. First bracket: $63÷9=7$.
4. Value: $7\times 21=147$.

Trick: Answer must be a multiple of 7 (first bracket = 7): only 147 qualifies.

Answer: (D) 147

Concept: A number divisible by several numbers is a multiple of their LCM.

1. $12=2^2·3$, $20=2^2·5$, $25=5^2$ → $\text{LCM}=4\times 3\times 25=300$.
2. Multiples of 300 below 1000: 300, 600, 900 → X = 900.
3. Digit sum = 9.

Trick: 999 ÷ 300 leaves 99 → X = $999-99=900$.

Answer: (B) 9

Concept: Overheads are added to the purchase price to get the cost price.

1. $\text{CP}=22,400+1,600=$ ₹24,000.
2. Gain = $28,500-24,000=$ ₹4,500.
3. $\text{Profit}\%=\frac{4500}{24000}\times 100=18.75\%$.

Trick: $\frac{4500}{24000}=\frac{3}{16}=18.75\%$ (remember $\frac{1}{16}=6.25\%$).

Answer: (D) 18.75%

Concept: Compare one-day work of the two groups to relate a man's and a woman's efficiency.

1. Daily rates are in ratio $\frac{1}{6}:\frac{1}{4}=2:3$, so $3(4M+3W)=2(5M+7W)\to 12M+9W=10M+14W\to 2M=5W$.
2. Take M = 5 units, W = 2 units/day. Job = $6\times (20+6)=156$ units.
3. 8 men + 6 women do $40+12=52$ units a day.
4. Time = $156÷52=3$ days.

Trick: Use $2M=5W$: $8M+6W=26W$ which is exactly double of $4M+3W$ (13W) → half of 6 days = 3.

Answer: (B) 3 days

Concept: Multiply the successive factors on a base of 100.

1. Factors: $0.60\times 0.50\times 0.85\times 1.40$.
2. 100 → 60 → 30 → 25.5 → 35.7.
3. Change = $35.7-100=-64.3$ → decrease of 64.3%.

Trick: Three falls then one 40% rise can never give an overall increase → (b), (c) out at once.

Answer: (A) Decreases by 64.3%

Concept: $\text{Average speed}=\text{total distance}÷\text{total time}$.

1. Times: $\frac{8}{12}+\frac{8}{18}+\frac{8}{24}+\frac{8}{36}$ hr. LCM 72 → $\frac{48+32+24+16}{72}=\frac{120}{72}=\frac{5}{3}$ hr.
2. Distance = 32 km.
3. Speed = $32\times \frac{3}{5}=19.2$ km/hr.

Trick: For equal distances, average = harmonic mean = $4÷(\frac{1}{12}+\frac{1}{18}+\frac{1}{24}+\frac{1}{36})=4\times \frac{72}{15}=19.2$.

Answer: (A) 19.2

Concept: For a fixed distance, $\text{time}\propto \frac{1}{\text{speed}}$.

1. Speeds 3 : 5 → times 5 : 3.
2. B's 3 parts = 18 min → 1 part = 6 min.
3. A = $5\times 6=30$ min.

Trick: Slower walker needs more than 18 min – and $18\times \frac{5}{3}$ is the only whole fit: 30.

Answer: (D) 30 min

Concept: If c is third proportional to a, b: $\frac{a}{b}=\frac{b}{c}$, i.e. $b^2=a·c$.

1. $(x+100{)}^2=405x$.
2. $x^2-205x+10000=0\to (x-125)(x-80)=0$.
3. $x>100\to x=125$.

Trick: Check options: $x=125\to (225{)}^2=50625=405\times 125$ ✓.

Answer: (B) 125

Concept: Speed becomes $\frac{3}{4}$ → time becomes $\frac{4}{3}$ of usual.

1. Extra time = $\frac{4}{3}-1=\frac{1}{3}$ of usual time.
2. $\frac{1}{3}\times T=33$ min.
3. T = 99 min.

Trick: Speed $\frac{a}{b}$ of normal → normal time = $\text{delay}\times \frac{a}{b-a}=33\times \frac{3}{1}=99$.

Answer: (C) 99

Concept: CSA of hemisphere = $2\pi r^2$ (base not included).

1. $r=13\sqrt{3}\to r^2=169\times 3=507$.
2. $\text{CSA}=2\pi \times 507=1014\pi {\text{cm}}^2$.

Trick: Total surface area would be $3\pi r^2$; curved only = $2\pi r^2$.

Answer: (A) $1014\pi {\mathrm{cm}}^2$

Concept: $\text{CI}-\text{SI}$ for 2 years = interest earned on the 1st year's interest.

1. SI per year = $40÷2=$ ₹20.
2. Difference $65-40=$ ₹25 $=20\times \frac{R}{100}\to R=125\%$.
3. P = SI per year ÷ rate = $20÷1.25=$ ₹16.

Trick: $R=2\times \frac{\text{CI}-\text{SI}}{\text{SI}}\times 100=2\times \frac{25}{40}\times 100=125\%$.

Answer: (B) 16

Concept: New member = new total − old total.

1. Old sum = $39\times 39=1521$.
2. New sum = $40\times 40=1600$.
3. Teacher = $1600-1521=79$ years.

Trick: Teacher = old average + (new count × rise) = $39+40\times 1=79$.

Answer: (C) 79

Concept: ÷ and × left to right first, then −.

1. $32÷8=4$, then $4\times 4=16$.
2. $3\times 4=12$.
3. $16-12=4$.

Trick: Never do $8\times 4$ first – division comes earlier when it is on the left.

Answer: (C) 4

Concept: $\text{SP}=\text{MP}\times \frac{100-\text{discount}}{100}$.

1. SP of one device = $14430÷5=$ ₹2,886.
2. $\text{MP}=2886\times \frac{100}{74}=$ ₹3,900.

Trick: ₹2,886 is the trap (that's the SP of one); MP must be higher.

Answer: (B) ₹3,900

Concept: Third proportional to a and b = $\frac{b^2}{a}$.

1. $(4xy{)}^2÷3x^2=\frac{16x^2{y}^2}{3x^2}=\frac{16y^2}{3}$.
2. $\frac{16y^2}{3}=48\to y^2=9$.
3. y = 3.

Trick: x cancels completely – only y remains, so solve $16y^2=144$ directly.

Answer: (D) 3

Concept: After a 25% cut, price = $\frac{3}{4}$ of original.

1. $22200÷4=5550$ (the 25% part).
2. $22200-5550=$ ₹16,650.

Trick: $25\%=\frac{1}{4}$: divide by 4 and subtract.

Answer: (C) ₹16,650

Concept: Inner bracket first, then division/multiplication.

1. $(8-4)$ gives 4 → $\frac{19}{4}\times 4=19$.
2. $\frac{42}{3}=14$ → second bracket = $14+19=33$.
3. $42÷7=6$ → $6\times 33=198$.

Trick: Result must be a multiple of 6 → only 198 (180 is also, but $33\times 6\ne 180$).

Answer: (C) 198

Concept: Gain = $\text{SP}-\text{CP}$; compare in terms of 'chairs'.

1. $\text{SP}(151)-\text{CP}(151)=\text{SP}(51)\to \text{CP}(151)=\text{SP}(100)$.
2. Profit = SP of 51 chairs on a cost equal to SP of 100 chairs → $\frac{51}{100}\times 100=51\%$.

Trick: $\text{Profit}\%=\frac{\text{gain-count}}{\text{sold}-\text{gain-count}}\times 100=\frac{51}{151-51}\times 100=51\%$.

Answer: (D) 51%

Concept: Same rate and time → extra interest comes only from extra principal.

1. Extra principal = $9400-5400=$ ₹4,000.
2. $\frac{4000\times R\times 3}{100}=840\to 120R=840$.
3. R = 7%.

Trick: Per year extra = $\frac{840}{3}=280$; $\frac{280}{4000}=7\%$.

Answer: (B) 7

Concept: For 3 years: $\text{CI}-\text{SI}=P\times {\left(\frac{R}{100}\right)}^2\times (3+\frac{R}{100})$.

1. R = 4% → $(0.04{)}^2\times 3.04=0.0016\times 3.04=0.004864$.
2. $P\times 0.004864=228$.
3. $P=228÷0.004864=$ ₹46,875.

Trick: Check by last digits: $46875\times 0.004864=228$ exactly; others give non-round values.

Answer: (A) 46875