Jawahar Navodaya Examination Preparation 2026

  Question 60: Multiply by 0.01 Q60: 140.75 × 0.01 = ? 140.75 \times 0.01 = ? 140.75 × 0.01 = ? Options: (a) 140.75 (b) 14000.75 (c) 1.4075 (d) 0.14075 📝 Step 1: Understand multiplication by 0.01 Multiplying by 0.01 is the same as dividing by 100 . 140.75 × 0.01 = 140.75 100 140.75 \times 0.01 = \frac{140.75}{100} 140.75 × 0.01 = 100 140.75 ​ 📝 Step 2: Move the decimal Decimal moves 2 places to the left (because 0.01 = 1/100): 140.75 → 1.4075 140.75 \rightarrow 1.4075 140.75 → 1.4075 ✅ Step 3: Answer Answer: (c) 1.4075 ✅ 💡 Quick Tip Multiplying by 0.1 → move decimal 1 place left Multiplying by 0.01 → move decimal 2 places left Multiplying by 0.001 → move decimal 3 places left

  💰 Question 59: Simple Interest Problem Q59: In how many years does a sum of ₹1200 become ₹1800 at a simple interest rate of 5% per annum ? Options: (a) 10 years (b) 20 years (c) 15 years 📝 Step 1: Recall the simple interest formula Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) 100 \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} Simple Interest (SI) = 100 Principal (P) × Rate (R) × Time (T) ​ We are given: Principal P = 1200 P = 1200 P = 1200 Final Amount A = 1800 A = 1800 A = 1800 Rate R = 5 % R = 5\% R = 5% per annum 📝 Step 2: Find the simple interest SI = Amount − Principal = 1800 − 1200 = 600 \text{SI} = \text{Amount} - \text{Principal} = 1800 - 1200 = 600 SI = Amount − Principal = 1800 − 1200 = 600 ✅ So, the interest earned = ₹600 📝 Step 3: Use SI formula to find time S I = P × R × T 100 SI = \frac{P \times R \times T}{...

  🔢 Question 58: Prime Factorization of 640 Q58: Find the prime factorization of 640 . Options: (a) 2 × 2 × 2 × 2 × 2 × 5 (b) 2 × 2 × 2 × 2 × 2 × 2 × 5 (c) 2 × 2 × 2 × 2 × 2 × 5 × 5 (d) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 📝 Step 1: Start dividing by the smallest prime (2) We know 640 is even , so divide by 2 repeatedly until we cannot: 640 ÷ 2 = 320 ✅ 320 ÷ 2 = 160 ✅ 160 ÷ 2 = 80 ✅ 80 ÷ 2 = 40 ✅ 40 ÷ 2 = 20 ✅ 20 ÷ 2 = 10 ✅ 10 ÷ 2 = 5 ✅ Now we are left with 5 , which is a prime number. 📝 Step 2: Write all prime factors We divided by 2 seven times , and then we have 5 left. 640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 ✅ Or in exponent form: 640 = 2 7 × 5 640 = 2^7 × 5 640 = 2 7 × 5 ✅ Step 3: Match with the options The correct answer is: (d) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 ✅ 💡 Quick Tip for Prime Factorization Start dividing by the smallest prime (2, then 3, 5, 7…) Keep div...

  ⏰ Question 57: Finding the Start Time Q57: We reached our destination at 2:45 pm after travelling for 4 ½ hours . When did we start? Options: (a) 9:00 am (b) 10:00 am (c) 10:15 am (d) 8:15 am 📝 Step 1: Understand the problem We know: End time (destination time) = 2:45 pm Travel time = 4½ hours = 4 hours 30 minutes We need to find the start time . 💡 Tip: To find the start time, subtract the travel time from the arrival time . 📝 Step 2: Convert mixed fraction to hours and minutes 4 1 2  hours = 4  hours  30  minutes 4 \frac{1}{2} \text{ hours} = 4 \text{ hours } 30 \text{ minutes} 4 2 1 ​  hours = 4  hours  30  minutes 📝 Step 3: Subtract hours first End time: 2:45 pm Subtract 4 hours: 2 : 45 − 4 : 00 = 10 : 45 a m 2:45 - 4:00 = 10:45 am 2 : 45 − 4 : 00 = 10 : 45 am 📝 Step 4: Subtract minutes Now subtract 30 minutes: 10 : 45 − 0 : 30 = 10 : 15 a m 10:45 - 0:30 = 10:15 am 10 : 45 − 0 : 30 = 10 : 15 am ...

  🧱 Question 56: How Many Bricks Are Needed? Q56: How many bricks will be required for a wall 8 m long, 6 m high, and 22.5 cm thick , if each brick measures 25 cm × 11.25 cm × 6 cm ? Options: (a) 640 (b) 1380 (c) 6400 (d) 7600 📝 Step 1: Convert all dimensions to the same unit We have: Wall: 8 m × 6 m × 22.5 cm Brick: 25 cm × 11.25 cm × 6 cm Tip: Always use the same unit . Let’s use cm : 1  m = 100  cm 1 \text{ m} = 100 \text{ cm} 1  m = 100  cm Wall dimensions in cm: Length = 8 × 100 = 800 cm Height = 6 × 100 = 600 cm Thickness = 22.5 cm (already in cm) 📝 Step 2: Find the volume of the wall Volume of wall = length × height × thickness \text{Volume of wall} = \text{length} \times \text{height} \times \text{thickness} Volume of wall = length × height × thickness V wall = 800 × 600 × 22.5 V_\text{wall} = 800 \times 600 \times 22.5 V wall ​ = 800 × 600 × 22.5 Step by step: 800 × 600 = 480,000 480,000...

Q: A square and a rectangle have the same perimeter . If the side of the square is 16 m and the length of the rectangle is 18 m , find the breadth of the rectangle . Options: (a) 14 m (b) 15 m (c) 16 m (d) 17 m 📝 Step-by-Step Solution Step 1: Understand the problem We have: Square side = 16 m Rectangle length = 18 m Both shapes have the same perimeter Find rectangle breadth Step 2: Recall formulas Perimeter of a square = 4 × side Perimeter of a rectangle = 2 × (length + breadth) 💡 Tip: Perimeter = total distance around the shape. Step 3: Find the square's perimeter P square = 4 × 16 = 64  m P_\text{square} = 4 \times 16 = 64 \text{ m} P square ​ = 4 × 16 = 64  m Step 4: Set up the rectangle’s perimeter P rectangle = 2 × ( length + breadth ) P_\text{rectangle} = 2 \times (\text{length} + \text{breadth}) P rectangle ​ = 2 × ( length + breadth ) Since both perimeters are equal: 2 × ( 18 + breadth ) = 64 2 \times (18 + \text{brea...

  Question: Amit bought a table for ₹1200 and spent ₹200 on its repair. He sold it for ₹1680. What is his profit or loss percentage? Options: (a) 12% profit (b) 16 ⅔% profit (c) 20% loss (d) 20% profit Step 1: Find the Total Cost Price (CP) The total cost price includes the price of the table plus repair cost : Total CP = 1200 + 200 = 1400 \text{Total CP} = 1200 + 200 = 1400 Total CP = 1200 + 200 = 1400 Step 2: Find the Selling Price (SP) SP = 1680 \text{SP} = 1680 SP = 1680 Step 3: Determine Profit or Loss Profit = S P − C P = 1680 − 1400 = 280 \text{Profit} = SP - CP = 1680 - 1400 = 280 Profit = SP − CP = 1680 − 1400 = 280 Since SP > CP, Amit made a profit . Step 4: Calculate Profit Percentage Profit % = Profit CP × 100 = 280 1400 × 100 = 20 % \text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{280}{1400} \times 100 = 20\% Profit % = CP Profit ​ × 100 = 1400 280 ​ × 100 = 20% ✅ Answer: (d) 20% profit Fast Calculation T...

  Question: One-fourth of birds of a flock are at a river bank and one-fifth of that flock are in their nest. The remaining 22 birds are wandering in search of food. What is the number of birds in their nest? Options: (a) 40 (b) 18 (c) 10 (d) 8 Step 1: Let’s Assign a Variable Let the total number of birds in the flock be x x x . Birds at river bank = 1 4 x \frac{1}{4}x 4 1 ​ x Birds in nest = 1 5 x \frac{1}{5}x 5 1 ​ x Birds wandering = 22 We know that all birds together = birds at river + birds in nest + wandering birds: 1 4 x + 1 5 x + 22 = x \frac{1}{4}x + \frac{1}{5}x + 22 = x 4 1 ​ x + 5 1 ​ x + 22 = x Step 2: Solve the Equation Combine fractions: 1 4 x + 1 5 x = 5 + 4 20 x = 9 20 x \frac{1}{4}x + \frac{1}{5}x = \frac{5 + 4}{20}x = \frac{9}{20}x 4 1 ​ x + 5 1 ​ x = 20 5 + 4 ​ x = 20 9 ​ x So the equation becomes: 9 20 x + 22 = x \frac{9}{20}x + 22 = x 20 9 ​ x + 22 = x Subtract 9 20 x \frac{9}{20}x 20 9 ​ x from both sides: 22 = x − 9 20 x = 11 20...

  Question: A park is 1500 m long and 750 m wide. A cyclist has to take four rounds of this park. How much time will he take at a speed of 4.5 km/h? Options: (a) 40 h (b) 20 h (c) 10 h (d) 4 h Step 1: Understanding the Problem Like a Kid Imagine a big rectangle-shaped park. The cyclist rides around the park’s boundary — that’s like walking along the edge of a chocolate bar. To find out how far he will ride , we need the perimeter of the park. Formula for perimeter of a rectangle: Perimeter = 2 × ( Length + Width ) \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) Perimeter = 2 × ( Length + Width ) Here: Length = 1500 m Width = 750 m So, Perimeter = 2 × ( 1500 + 750 ) = 2 × 2250 = 4500  m \text{Perimeter} = 2 \times (1500 + 750) = 2 \times 2250 = 4500 \text{ m} Perimeter = 2 × ( 1500 + 750 ) = 2 × 2250 = 4500  m Think of it like: if you walk around the edge of your school 2 times (like 2 rectangles stuck together), you know the total path. ...

  Question 51: Find the approximate result of the expression (in whole numbers): 49.6 × 10.2 − 7.1 × 29.7 − 5.1 × 20.1 49.6 \times 10.2 - 7.1 \times 29.7 - 5.1 \times 20.1 49.6 × 10.2 − 7.1 × 29.7 − 5.1 × 20.1 Options: (a) 390 (b) 290 (c) 209 (d) 190 Step 1: Round the numbers for approximation 49.6 ≈ 50 49.6 \approx 50 49.6 ≈ 50 , 10.2 ≈ 10 10.2 \approx 10 10.2 ≈ 10 → 50 × 10 = 500 50 \times 10 = 500 50 × 10 = 500 7.1 ≈ 7 7.1 \approx 7 7.1 ≈ 7 , 29.7 ≈ 30 29.7 \approx 30 29.7 ≈ 30 → 7 × 30 = 210 7 \times 30 = 210 7 × 30 = 210 5.1 ≈ 5 5.1 \approx 5 5.1 ≈ 5 , 20.1 ≈ 20 20.1 \approx 20 20.1 ≈ 20 → 5 × 20 = 100 5 \times 20 = 100 5 × 20 = 100 Step 2: Perform the calculation 500 − 210 − 100 = 190 500 - 210 - 100 = 190 500 − 210 − 100 = 190 ✅ Answer: (d) 190 Tip for fast calculation: Round off numbers to the nearest whole number before multiplying. Do step-by-step subtraction after approximation. This gives a quick and reasonably accurate result for multipl...