RRB Technician Grade III 2024, 2025 PYQs

Concept: $\text{SP}=\text{MP}\times (1-d_1)(1-d_2)$; Profit % = $\frac{\text{Profit}}{\text{CP}}\times 100$.

1. SP of X = $800+901=$ ₹1701
2. $\text{MP}\times 0.27\times 0.63=1701\Rightarrow \text{MP}\times 0.1701=1701\Rightarrow \text{MP}=$ ₹10,000
3. SP of Y = 11% of 10,000 = ₹1100; profit = 300
4. Profit % = $\frac{300}{800}\times 100=37.5\%$

Trick: $0.27\times 0.63=0.1701$ and $\text{SP}=1701$, so $\text{MP}=10,000$ at a glance.

Answer: (D) 37.5%

Concept: Same direction: relative speed = difference of speeds; distance = sum of lengths.

1. Speed of 1st train = $\frac{180}{12}=15$ m/s
2. Relative speed = $\frac{180+120}{15}=20$ m/s ⇒ 2nd train = $15+20=35$ m/s
3. $35\times \frac{18}{5}=126$ km/h

Trick: To convert m/s to km/h multiply by $\frac{18}{5}$: $35\times 3.6=126$.

Answer: (C) 126 km/h

Concept: Area = $\frac{1}{2}\times$ (sum of parallel sides) $\times$ height.

1. $\frac{1}{2}\times (a+b)\times 52=988\Rightarrow a+b=38$
2. $a-b=9$
3. $a=\frac{38+9}{2}=23.5$, $b=14.5$ cm

Trick: Check the options: the sides must add up to 38 and differ by 9, which fits only 23.5 and 14.5.

Answer: (B) 23.5, 14.5

Concept: Half-yearly: rate = $\frac{R}{2}$ and time periods = $2n$.

1. Rate = 10% per half-year, 2 periods
2. $A=42000\times (1.1{)}^2=42000\times 1.21$
3. $A=$ ₹50,820

Trick: Two periods at 10% give an effective rate of 21%. 21% of 42,000 = 8,820, so the amount is 50,820.

Answer: (A) ₹50,820

Concept: Fourth proportional of a, b, c is d where a : b = c : d, so $d=\frac{bc}{a}$.

1. $y=\frac{3x\times 12}{2x}$
2. $=\frac{36}{2}=18$

Trick: x cancels: 2 : 3 = 12 : y gives $y=12\times \frac{3}{2}=18$.

Answer: (B) 18

Concept: For two numbers: HCF × LCM = product of the numbers.

1. LCM = $98304÷128$
2. $=768$

Trick: The LCM must be a multiple of the HCF (128): $768=128\times 6$ and no other option is. Pick 768 without dividing.

Answer: (B) 768

Concept: Increased by 110% means the new value is 210% of the original.

1. $2.1\times x=3570$
2. $x=3570÷2.1=1700$

Trick: Check: 1700 + 110% of 1700 = $1700+1870=3570$ ✓

Answer: (D) 1700

Concept: Gain factor = (1 + profit%) × (claimed weight/actual weight).

1. Gives 86 g for every 100 g; charges 115% of the cost of 100 g
2. Profit factor = $\frac{115}{86}=1.3372$
3. Profit ≈ $33.72\%\approx 34\%$

Trick: Think of it as a sale of 86 at a price of 115: profit = $\frac{29}{86}\times 100\approx 33.7\%$.

Answer: (C) 34%

Concept: Each spend of a percentage of the 'remaining' amount multiplies the income by $(1-p\%)$.

1. After food + education (40%): $0.6x$
2. After shopping/transport (40% of rest): $0.6\times 0.6x=0.36x$
3. After medical (20% of rest): $0.36\times 0.8x=0.288x=23,040$
4. $x=23040÷0.288=$ ₹80,000

Trick: Check the option: 80,000 → 48,000 → 28,800 → 23,040 ✓

Answer: (C) ₹80,000

Concept: $P=\frac{SI\times 100}{R\times T}$.

1. $P=\frac{720\times 100}{8\times 3}$
2. $=\frac{72000}{24}=$ ₹3000

Trick: SI for 3 years at 8% = 24% of P. $24\%=720$, so $1\%=30$ and $P=3000$.

Answer: (C) 3000

Concept: Find the cost of one item, then divide the money available by it.

1. Cost of 1 notebook = $240÷15=$ ₹16
2. Notebooks for ₹992 = $992÷16=62$

Trick: $992÷16$: $16\times 60=960$, remaining $32=16\times 2$, so 62.

Answer: (A) 62

Concept: The expression is ${27}^3-{22}^3$ (cubes); use $a^3-b^3=(a-b)(a^2+ab+b^2)$.

1. $a-b=27-22=5$
2. $a^2+ab+b^2=729+594+484=1807$
3. ${27}^3-{22}^3=5\times 1807=9035$

Trick: Unit digit check: $7^3$ ends in 3, $2^3$ ends in 8 → $13-8$ → unit digit 5. Only 9035 ends in 5.

Answer: (A) 9035

Concept: Sides $n={360}^{\circ }÷$ exterior angle; diagonals = $\frac{n(n-3)}{2}$.

1. $n=360÷40=9$ sides
2. Diagonals = $\frac{9\times (9-3)}{2}=\frac{9\times 6}{2}=27$

Yaad rakhein: Sum of exterior angles of any polygon is always 360°.

Answer: (A) 27

Concept: Convert the past sum to the present sum, then use $\frac{\text{sum}-\text{difference}}{2}$ for the younger.

1. 5 years ago sum = 30 → present sum = $30+5+5=40$
2. Difference = 26
3. Nidhi (younger) = $\frac{40-26}{2}=7$ years

Trick: $\text{Younger}=\frac{\text{Sum}-\text{Difference}}{2}$; $\text{Older}=\frac{\text{Sum}+\text{Difference}}{2}$.

Answer: (D) 7

Concept: Empirical relation: Mode = 3 Median − 2 Mean.

1. Mode = $3\times 30-2\times 20$
2. $=90-40=50$

Yaad rakhein: Mean − Mode = 3(Mean − Median). Here $20-50=3(20-30)=-30$ ✓.

Answer: (B) 50

Concept: Find $\sqrt{225}+\sqrt{0.04}-\sqrt{4.84}$ using known squares.

1. $\sqrt{225}=15$
2. $\sqrt{0.04}=0.2$ (since ${0.2}^2=0.04$)
3. $\sqrt{4.84}=2.2$ (since ${22}^2=484$)
4. $15+0.2-2.2=13$

Trick: Decimal places of a square root = half of those in the number (4.84 has 2 → root has 1).

Answer: (C) 13

Concept: Find the cost of one pen, then multiply.

1. Cost of 1 pen = $136÷8=$ ₹17
2. Cost of 12 pens = $17\times 12=$ ₹204

Trick: 12 pens = 8 pens $\times \frac{3}{2}$ → $136\times \frac{3}{2}=$ ₹204.

Answer: (D) ₹204

Concept: Write x as a perfect square: $5+2\sqrt{6}=(\sqrt{3}+\sqrt{2}{)}^2$.

1. $\sqrt{x}=\sqrt{3}+\sqrt{2}$
2. $\frac{1}{\sqrt{x}}=\frac{1}{\sqrt{3}+\sqrt{2}}=\sqrt{3}-\sqrt{2}$
3. $\frac{x-1}{\sqrt{x}}=\sqrt{x}-\frac{1}{\sqrt{x}}=(\sqrt{3}+\sqrt{2})-(\sqrt{3}-\sqrt{2})=2\sqrt{2}$

Trick: For $a+2\sqrt{b}$, find two numbers with sum a and product b: $3+2=5$, $3\times 2=6$ → $\sqrt{3}+\sqrt{2}$.

Answer: (D) $2\sqrt{2}$

Concept: Solve brackets first, then ÷ and × from left to right, then + and −.

1. $\frac{5}{6}+\frac{1}{3}=\frac{7}{6}$; $\frac{2}{5}+0.3=0.7=\frac{7}{10}$
2. $\frac{7}{6}÷\frac{7}{10}=\frac{10}{6}=\frac{5}{3}$
3. $\frac{5}{3}\times 0.5=\frac{5}{6}$
4. $\frac{5}{6}+\frac{1}{2}-\frac{1}{6}=\frac{5}{6}+\frac{3}{6}-\frac{1}{6}=\frac{7}{6}$

Yaad rakhein: ÷ and × have equal priority – do them strictly left to right.

Answer: (C) $\frac{7}{6}$

Concept: Net work per hour = filling rate − emptying rate.

1. Net rate = $\frac{1}{11}-\frac{1}{22}=\frac{2-1}{22}=\frac{1}{22}$
2. Time = 22 hours

Trick: Time = $\frac{a\times b}{b-a}=\frac{11\times 22}{22-11}=22$ h.

Answer: (B) 22