Squares and Square Roots Test

Result

Squares and Square Roots Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If the three numbers are in the ratio 2 : 3 : 5, so that the sum of their squares is 608. Find the numbers respectively.

A
8, 12, 20

B
12, 8, 20

C
20, 8, 12

D
20, 12, 8

Solution

Let the numbers be 2x, 3x and 5x. According to question, we have (2x)² + (3x)² + (5x)² = 608 ⇒4x² + 9x² + 25x² = 608 ⇒38x² = 608 ⇒x² = 608/38= 16 ⇒ x = 4

Hence, the numbers are 8, 12 and 20.
Question 2
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A certain number of men went to a hotel. Each man spent as many rupees as one-fourth of the men. If the total bill paid was Rs.20449, then how many men visited the hotel?

A
286

B
284

C
281

D
283

Solution

Let number of men visited hotel be x. ∴ Each man spent =Rs.(x/4) According to question, x(x/4) = 20449 ⇒ x² = 20449 × 4 ⇒ x²81796 ⇒ x = 286 ∴ Number of men visited hotel = 286
Question 3
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A general arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row.

A
81

B
90

C
80

D
91

Solution

Let x be the number of soldiers in each row. To form a perfect square, number of soldiers in each row must be equal to the number of rows. According to question, Number of soldiers who form square =8160 - 60 = 8100 ∴ x × x = 8100 ⇒ x² = 8100⇒ x = 90 ∴ Number of soldiers in each row = 90
Question 4
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A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to Rs.59.29, the number of members in the group is ____.

A
57

B
67

C
77

D
87

Solution

Let the number of members be x. Then, the amount received from each member = x paise. Now, total collection =x² paise ⇒(59.29 × 100) paise = x² paise ⇒ 5929 = x²⇒ x = 77

So, number of members = 77