Question

The rainfall in Jhunjhunu for the last two days was in the ratio of 2 : 3. The average rainfall for the first five days was recorded to be 0.83 cm. The average rainfall of all seven days was 0.80 cm. If n is the rainfall on the 7^th day, which of the following is/are correct?

A. n is a perfect square

B. n/10 is a perfect cube

C. n – 2 is a perfect square

D. n = 8.7 mm

1. Only A
2. B, C, and D
3. B and C
4. Only D

Answer 1

Correct Answer - Option 4 : Only D

Given:

Ratio of rainfall for 6^th and 7^th day = 2 ∶ 3

Average rainfall for the first five days = 0.83 cm

Average rainfall for 7 days = 0.80 cm

Formula Used:

Average = Sum of values/Number of values

Calculation:

Let the rainfall on 6^th day be 2y and on 7^th day be 3y

Sum of recorded rainfall for the first five days = 0.83 × 5

⇒ Sum of recorded rainfall for the first five days = 4.15

Sum of recorded rainfall for 7 days = 0.80 × 7

⇒ Sum of recorded rainfall for 7 days = 5.60

⇒ 4.15 + 2y + 3y = 5.60

⇒ 5y = 1.45

⇒ y = 0.29

Rainfall on 6^th day = 2 × 0.29

⇒ 0.58 cm

Rainfall on 7^th day = 3 × 0.29

⇒ 0.87 cm

⇒ n = 0.87 cm

A. n is a perfect square

0.87 is not a perfect square

⇒ A is not correct

B. n/10 is a perfect cube

0.87/10 = 0.087

⇒ B is not correct

C. n – 2 is a perfect square

0.87 – 2 = -1.13

⇒ C is not correct

D. n = 87 mm

n = 0.87 × 10 mm

⇒ 8.7 mm

⇒ D is correct

∴ Only D is correct.