Class 7 Maths Chapter 3 HOTS Question Answer - A Peek Beyond the Point

Q1: A shopkeeper sells rice in packets of 0.75 kg, 1.25 kg, and 2.5 kg. Arjun needs exactly 4.75 kg of rice for a recipe. Determine the combination of packets he should buy to get exactly 4.75 kg, minimising the number of packets. Justify your choice.

Sol:

• Two 2.5 kg packets = 5.0 kg → too much.

• 2.5 + 1.25 + 0.75 = 4.5 kg → too little.

• 2.5 + 1.25 + 1.25 = 5.0 kg → too much.

• 2.5 + 0.75 + 0.75 + 0.75 = 4.75 kg → exact match (4 packets).

• 1.25 + 1.25 + 0.75 + 0.75 + 0.75 = 4.75 kg → exact match (5 packets).

• Best solution: 1 packet of 2.5 kg + 3 packets of 0.75 kg = 4.75 kg.
  This uses only 4 packets, which is the minimum.
  

Q2: A sequence of decimal numbers is given as 3.6, 4.2, 4.8, 5.4. The pattern continues, but the increment doubles after the fourth term. Find the next three terms of the sequence and explain the new pattern. 

Sol: Initial pattern: Each term increases by 0.6: 3.6 + 0.6 = 4.2, 
4.2 + 0.6 = 4.8, 
4.8 + 0.6 = 5.4. 
After the fourth term (5.4), the increment doubles: 0.6 × 2 = 1.2. 
Next terms: 
- 5.4 + 1.2 = 6.6 
- 6.6 + 1.2 = 7.8 
- 7.8 + 1.2 = 9.0

Q3: A carpenter is tasked with cutting a wooden plank to 3.65 meters, but due to a decimal point misreading, he cuts it to 36.5 meters. Calculate the difference in length and discuss the impact of this error in a real-world context, such as building a bridge support.

Sol: Intended length = 3.65 m. 
Actual length = 36.5 m. 
Difference = 36.5 − 3.65 = 32.85 meters

Q4: A tailor needs 245.6 cm of cloth but the shop sells cloth in meters. The tailor buys 2.5 meters of cloth. Does he have enough cloth? If not, how much more does he need in centimeters? 

Sol: Convert 2.5 meters to centimeters: 
1 meter = 100 cm, 
so 2.5 × 100 = 250 cm. 
The tailor needs 245.6 cm. 
Compare: 250 cm > 245.6 cm, so he has enough cloth. 
Extra cloth = 250 − 245.6 = 4.4 cm.

Q5: A school track is marked with a rope that is 156.8 cm long, but the measurement must be in meters for the sports rulebook. The coach rounds 156.8 cm to the nearest meter for simplicity. What is the rounded length ?

 Sol: Convert 156.8 cm to meters: 1 meter = 100 cm, 
so 156.8 ÷ 100 = 1.568 meters. 
Round to the nearest meter: 1.568 is closer to 2 than 1 (since 0.568 > 0.5). 
So, rounded length = 2 meters.