CUET 2026 Numbers & Quantification: Fast Tricks for Modulo, Alligation, Boats & Pipes

Numbers & Quantification covers a wide range of topics in CUET Section B2 — but the questions are almost always mechanical once you know the right setup. This post gives you the exact template for each topic so you're not figuring out the method under exam pressure.

The Cycle Trick for Last Digits

Powers of numbers repeat their last digits in a cycle. Memorise these:

How to use it:

What is the last digit of $2^{53}$?

Cycle length = 4. $53 \div 4$ → remainder 1 → first digit in cycle = 2

Last digit of $2^{53}$ = 2.

2. Alligation — The "X Method" for Mixtures

Alligation gives the ratio in which two ingredients (cheaper and dearer) must be mixed to achieve a target mean value.

Where:

• $C$ = price/concentration of cheaper ingredient
• $D$ = price/concentration of dearer ingredient
• $M$ = target mean price/concentration

Visual Setup (draw this every time)

     C           D
      \         /
       \       /
        M (mean)
       /       \
      /         \
  (D - M)   (M - C)

Example: Mix milk worth ₹16/litre with milk worth ₹24/litre to get a mixture worth ₹20/litre. In what ratio?

3. Boats & Streams

Two speeds to know:

Where $u$ = boat speed in still water, $v$ = stream speed.

The Two Standard Question Types

Type 1 — Find upstream/downstream speed: Direct substitution.

Boat speed = 10 km/h, stream = 2 km/h → Upstream = 10 − 2 = 8 km/h

Type 2 — Find boat speed or stream speed given two times:

Use these recovery formulas if the question gives you speeds in both directions.

4. Pipes & Cisterns (Work Rate Method)

This is a rates problem — always work in "fraction of tank filled per hour."

The Three Steps

1. Convert each pipe to a rate (1/time)
2. Add rates for filling pipes; subtract rates for emptying pipes
3. Invert the combined rate to get the total time

Example: Pipe A fills in 6 hours, Pipe B fills in 3 hours. Together:

Common Trap: Emptying Pipe

If one pipe empties the tank, its rate is subtracted:

Side-by-Side Comparison: Boats vs Pipes

Both follow the same logic: combine quantities, then solve for time. Don't overthink the setup.

Quick Practice MCQs

Q1. What is the remainder when 57 is divided by 8?

• A) 1 ✓   B) 2   C) 3   D) 4

8 × 7 = 56, so 57 − 56 = 1

Q2. A boat's speed in still water is 10 km/h and the stream speed is 2 km/h. What is the upstream speed?

• A) 12   B) 10   C) 8 ✓   D) 6

Upstream = 10 − 2 = 8 km/h

Q3. Pipe A fills a tank in 6 hours, Pipe B in 3 hours. Together they fill the tank in:

• A) 2 hours ✓   B) 3 hours   C) 4 hours   D) 6 hours

Rates: 1/6 + 1/3 = 1/2 → Time = 2 hours

What's Next?

In Part 3, we cover Probability Distributions and Descriptive Statistics — Binomial, Poisson, Normal, and the basic measures of central tendency and spread. All with CUET-specific recognition triggers so you know which formula to reach for instantly.