RRB NTPC Graduate CBT 2 2024 PYQs

Concept: If $x$ varies inversely as $(y^3-1)$, then $x(y^3-1)=k$ (constant).

1. At $y=4$: $y^3-1=63$ → $k=6\times 63=378$.
2. At $y=8$: $y^3-1=511$.
3. $x=\frac{378}{511}=\frac{54}{73}$ (divide by 7).

Trick: $378=7\times 54$ and $511=7\times 73$.

Answer: (D) $\frac{54}{73}$

Concept: Find the cost price of the mixture from the selling price and profit, then use alligation.

1. CP of mixture $=\frac{91}{1.30}=70$ per kg.
2. Ghee: $70-56=14$; Oil: $112-70=42$.
3. Ghee : Oil $=14:42=1:3$.

Trick: Alligation always uses the mean cost price, never the selling price.

Answer: (D) 1 : 3

Concept: Value after $n$ years $=P{(1-\frac{r}{100})}^n$.

1. $P=100000$, $r=10$, $n=2$.
2. Value $=100000\times 0.9\times 0.9=100000\times 0.81$.
3. $=81000$.

Trick: Two successive 10% falls = $19\%$ fall ($10+10-1$).

Answer: (B) ₹81,000

Concept: $39=3\times 13$, so the number must be divisible by both 3 and 13.

1. 625092: digit sum $=6+2+5+0+9+2=24$ → divisible by 3.
2. $625092÷13=48084$ exactly ($13\times 48084=625092$) → divisible by 13.
3. Hence divisible by 39: $625092=39\times 16028$. Others fail (e.g. 625649 has digit sum 32, not divisible by 3).

Trick: Use the digit-sum test for 3 to cut options quickly, then divide only the survivors by 13.

Answer: (D) 625092

Concept: If two numbers are in ratio $a:b$ (co-prime) with HCF $h$, the numbers are $ha$ and $hb$, and LCM $=h\times a\times b$.

1. Numbers $=5\times 5=25$ and $5\times 4=20$.
2. LCM $=5\times 5\times 4=100$.
3. Check: $\text{HCF}\times \text{LCM}=5\times 100=500=25\times 20$ ✓.

Trick: LCM = HCF × product of ratio terms.

Answer: (C) 100

Concept: For equal distances at speeds $a,b,c$: average speed $=\frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$ (harmonic mean).

1. $\frac{1}{19}+\frac{1}{8}+\frac{1}{5}=\frac{40+95+152}{760}=\frac{287}{760}$.
2. Average $=\frac{3\times 760}{287}=\frac{2280}{287}$.
3. $2280=7\times 287+271$ → $7\frac{271}{287}\text{km/h}$.

Trick: Average speed must lie between 5 and 19 and below the plain average $10.67$ → only 7.9 fits.

Answer: (C) $7\frac{271}{287}\text{km/h}$

Concept: Bells ring together again after the LCM of their intervals.

1. $12=2^2\times 3$, $15=3\times 5$, $18=2\times 3^2$.
2. LCM $=2^2\times 3^2\times 5=180$ minutes $=3$ hours.
3. 10:00 am $+3$ h $=$ 1:00 pm.

Trick: LCM in minutes ÷ 60 gives the hours to add.

Answer: (C) 1:00 p.m.

Concept: $a^m\times b^m=(ab{)}^m$ and $a^{-m}=\frac{1}{a^m}$.

1. $7^{-8}\times {11}^{-8}\times {13}^{-8}=(7\times 11\times 13{)}^{-8}$.
2. $7\times 11\times 13=1001$.
3. So the value $={1001}^{-8}=\frac{1}{{1001}^8}$.

Trick: $7\times 11\times 13=1001$ – a number worth remembering.

Answer: (B) $\frac{1}{{1001}^8}$

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

1. $P=5000$, $R=5$, $T=2$.
2. $\text{SI}=\frac{5000\times 5\times 2}{100}=500$.

Trick: $5\%$ for 2 years = $10\%$ of 5000 = 500.

Answer: (B) 500

Concept: Successive changes multiply: final $=\text{original}\times (1\pm \frac{r_1}{100})\times (1\pm \frac{r_2}{100})\cdots$

1. Take original price $=100$.
2. $100\times 0.90\times 0.55\times 0.90=44.55$.
3. $44.55\times 1.65=73.5075$.
4. Change $=73.5075-100=-26.4925$ → decrease of about $26.49\%$.

Trick: Multiply the easy pair first: $0.9\times 0.9=0.81$, then $\times 0.55\times 1.65$.

Answer: (A) Decreases by $26.49\%$