The largest measuring cylinder that can accurately fill 3 tanks of capacity 98…
2024
The largest measuring cylinder that can accurately fill 3 tanks of capacity 98 , 182 & 266 liters each , is of capacity
Answer: C. 14 L — Answer: 14 liters Key idea: The largest measuring cylinder that can exactly fill all three tanks must be the highest common factor (HCF) of 98, 182 and 266…
- A.
2 L
- B.
7 L
- C.
14 L
- D.
98 L
Attempted by 201 students.
Show answer & explanation
Correct answer: C
Answer: 14 liters
Key idea: The largest measuring cylinder that can exactly fill all three tanks must be the highest common factor (HCF) of 98, 182 and 266 liters.
Find HCF of 98 and 182 using the Euclidean algorithm:
182 = 98 × 1 + 84
98 = 84 × 1 + 14
84 = 14 × 6 + 0 ⇒ HCF(98, 182) = 14
Now find HCF of the result 14 and 266:
266 = 14 × 19 + 0 ⇒ HCF(14, 266) = 14
Conclusion: HCF(98, 182, 266) = 14, so the largest measuring cylinder that can accurately fill all three tanks has capacity 14 liters.