Q&A: practice questions with answers

Concept: Solve the bracket first (BODMAS), then multiply, then subtract.

1. $91+26=117$
2. $\frac{96}{39}\times 117=96\times 3=288$ (since $117=39\times 3$)
3. $288-103=185$

Trick: Notice $117=3\times 39$ – the fraction cancels instantly.

Answer: (D) $185$

Concept: Remove the decimals by making both numbers have the same decimal places, then take square roots.

1. $\frac{\sqrt{0.028224}}{\sqrt{0.000784}}=\sqrt{\frac{28224}{784}}$
2. $\sqrt{28224}=168$ and $\sqrt{784}=28$
3. $\frac{168}{28}=6$

Trick: Both have 6 decimal places, so simply divide: $28224÷784=36$, and $\sqrt{36}=6$.

Answer: (C) $6$

Concept: Sum of ratio parts = total; find the value of one part.

1. Total parts $=16+10+9+17=52$
2. 1 part $=\frac{6292}{52}=121$
3. First + third $=(16+9)\times 121=25\times 121=3025$

Trick: Directly: $\frac{25}{52}\times 6292=3025$.

Answer: (A) 3025

Concept: Median = middle value after arranging data in order.

1. Ascending: 13, 25, 27, 28, 43, 57, 73, 77, 81, 87, 89
2. Number of terms $n=11$ (odd).
3. Median $={\left(\frac{n+1}{2}\right)}^{\text{th}}=6^{\text{th}}$ term $=57$

Yaad rakhein: Odd count → middle term; even count → average of two middle terms.

Answer: (A) 57

Concept: Sum of remaining = total sum − known parts.

1. Sum of first two $=2\times 77=154$
2. Remaining two $=655-154-128=373$
3. Average $=\frac{373}{2}=186.5$

Trick: Subtract what is known, then divide by the count left.

Answer: (B) 186.5

Concept: If savings are 17%, expenditure is the remaining 83% of salary.

1. Expenditure $\%=100-17=83\%$
2. Expenditure $=\frac{83}{100}\times 4900=83\times 49$
3. $=4067$

Trick: $83\times 49=83\times 50-83=4150-83=4067$.

Answer: (D) ₹4,067

Concept: Quarterly compounding: rate ÷ 4 per quarter, time × 4 quarters.

1. Rate per quarter $=\frac{20}{4}=5\%$, number of quarters $=4$
2. $A=480000\times (1.05{)}^4=480000\times 1.21550625=583443$
3. $CI=583443-480000=103443$

Trick: Effective rate for 5% over 4 periods $=21.550625\%$; $480000\times 0.21550625=103443$.

Answer: (A) ₹1,03,443

Concept: Net filling rate = filling rate − emptying rate.

1. Net rate $=\frac{1}{18}-\frac{1}{24}=\frac{4-3}{72}=\frac{1}{72}$ tank per hour
2. Full tank in 72 hours
3. One-fourth tank $=\frac{72}{4}=18$ hours

Trick: LCM method: capacity 72 units; fill +4, empty −3 → net 1 unit/h; $\frac{72}{4}=18$ units → 18 h.

Answer: (D) 18

Concept: Overtaking a man walking in the same direction: train length = (train speed − man speed) × time.

1. Let train speed $=v\text{km/h}$. Length is the same in both cases.
2. $(v-12.6)\times 12.5=(v-27)\times 14$
3. $12.5v-157.5=14v-378\Rightarrow 1.5v=220.5$
4. $v=147\text{km/h}$

Trick: The $\frac{5}{18}$ conversion cancels on both sides – solve directly in km/h.

Answer: (B) 147 km/hr

Concept: Dividend = divisor × quotient + remainder; HCF by repeated division.

1. Let smaller $=x$, greater $=6x+120$; difference $5x+120=2880\Rightarrow x=552$
2. Greater $=6\times 552+120=3432$
3. $3916-3432=484$; $3432=7\times 484+44$; $484=11\times 44$
4. HCF $=44$

Trick: HCF divides the difference: HCF divides $484=44\times 11$, and 44 divides both numbers.

Answer: (B) 44

Concept: When a transversal cuts two parallel lines, corresponding angles are equal.

1. One corresponding angle $={75}^{\circ }$.
2. Its corresponding angle at the other parallel line is also ${75}^{\circ }$.

Yaad rakhein: Parallel lines: corresponding = equal, alternate = equal, co-interior sum $={180}^{\circ }$.

Answer: (D) ${75}^{\circ }$

Concept: Stoppage time = time with stoppages − time without stoppages.

1. With stoppages: $\frac{528}{24}=22$ h
2. Without stoppages: $\frac{528}{88}=6$ h
3. Stoppage time $=22-6=16$ h

Trick: Per hour stoppage $=\frac{88-24}{88}=\frac{8}{11}$ h; $22\times \frac{8}{11}=16$ h.

Answer: (C) 16

Concept: If SP of $a$ articles = CP of $b$ articles, profit % $=\frac{b-a}{a}\times 100$.

1. Let CP of 1 book $=1$; then SP of 24 books $=30$
2. Gain on 24 books $=30-24=6$
3. Gain $\%=\frac{6}{24}\times 100=25\%$

Trick: SP of fewer items = CP of more items → always gain; $\frac{30-24}{24}=\frac{1}{4}$.

Answer: (A) $25\%$ gain

Concept: Solve innermost brackets first: ( ) → { } → [ ].

1. $28÷7=4$
2. $55-4=51$, then $51÷3=17$
3. $2+17=19$; $43+19=62$

Trick: Division inside the curly bracket comes after the bracket is solved.

Answer: (C) 62

Concept: Equal real roots when discriminant $D=b^2-4ac=0$.

1. $a=1,b=-6,c=k$
2. $(-6{)}^2-4\times 1\times k=0\Rightarrow 36=4k$
3. $k=9$

Trick: $x^2-6x+9=(x-3{)}^2$ – a perfect square has equal roots.

Answer: (C) 9

Concept: Net filling rate = filling rate − leaking rate.

1. Tap fills $\frac{1}{8}$ per hour; hole empties $\frac{1}{12}$ per hour.
2. Net rate $=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$.
3. Time to fill $=24$ hours.

Trick: Time $=\frac{a\times b}{b-a}=\frac{8\times 12}{12-8}=24$ h.

Answer: (D) 24 hours

Concept: Average $=\frac{\text{Sum of numbers}}{\text{Count}}$.

1. Sum $=14+16+27+31+39+44+51+58=280$.
2. Count $=8$.
3. Average $=\frac{280}{8}=35$.

Trick: Pair them: $14+58=72$, $16+51=67$, $27+44=71$, $31+39=70$ → total $280$.

Answer: (B) 35

Concept: Curved surface area of a cone $=\pi rl$ and $h=\sqrt{l^2-r^2}$.

1. $r=\frac{72}{2}=36\text{cm}$.
2. $\pi \times 36\times l=5904\pi \Rightarrow l=164\text{cm}$.
3. $h=\sqrt{{164}^2-{36}^2}=\sqrt{26896-1296}=\sqrt{25600}=160\text{cm}$.

Trick: ${164}^2-{36}^2=(164-36)(164+36)=128\times 200=25600$.

Answer: (B) 160

Concept: Mean of a frequency distribution $=\frac{\sum fx}{\sum f}$.

1. $\sum f=98+74+17+28+44=261$.
2. $\sum fx=1176+1628+986+2212+3916=9918$.
3. Mean $=\frac{9918}{261}=38$.

Trick: Check: $261\times 38=9918$ exactly.

Answer: (D) 38

Concept: Put $a=5k$, $b=3k$ and simplify.

1. $3a-2b=15k-6k=9k$.
2. $6a+2b=30k+6k=36k$.
3. Ratio $=9k:36k=1:4$.

Trick: Simply put $a=5$, $b=3$: $\frac{9}{36}=\frac{1}{4}$.

Answer: (D) 1 : 4