Test: Ratio and Proportion - Class 5 MCQ

A ratio equivalent to 3 : 7 is:
To find a ratio equivalent to 3 : 7, we need to find a pair of numbers that have the same ratio when simplified. Let's try the options:

(i) 3 : 9 → This simplifies to 1 : 3, not the same as 3 : 7
(ii) 6 : 10 → This simplifies to 3 : 5, not the same as 3 : 7
(iii) 9 : 21 → This simplifies to 3 : 7, which is the same as 3 : 7, so the answer is (iii).

The ratio 35 : 84 in simplest form is:
To simplify the ratio 35 : 84, we need to find the greatest common divisor (GCD) of 35 and 84, and then divide both numbers by this common divisor. Let's calculate:

GCD of 35 and 84 is 7.
Divide both numbers by 7: 35 ÷ 7 = 5, 84 ÷ 7 = 12.
So, the simplified ratio is 5 : 12, which corresponds to option (c).

In a class there are 20 boys and 15 girls. The ratio of boys to girls is:
To find the ratio of boys to girls, we simply put the number of boys first, followed by the number of girls. So, it's 20 : 15. However, to simplify the ratio, we can find the greatest common divisor (GCD) of 20 and 15 and divide both numbers by it:

GCD of 20 and 15 is 5.
Divide both numbers by 5: 20 ÷ 5 = 4, 15 ÷ 5 = 3.
So, the simplified ratio is 4 : 3, which corresponds to option (a).

Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is:

First, let's find the total parts in the ratio (7 + 9 = 16 parts).
Since the sum of the numbers is 112 and there are 16 parts in total, each part represents 
112/16=7
So, the larger number (which has 9 parts) is 
9x7=63
Therefore, the answer is (c) 63.

The ratio of 1.5 m to 10 cm is:

• To compare lengths, we should convert both lengths to the same unit. Let's convert 1.5 m to cm (since 1 m = 100 cm).
• 1.5m=1.5 x 100 cm =150 cm
• 1.5m=1.5x100cm =150cm.
• Now we have 150 cm to 10 cm. The ratio is 150:10
• To simplify, divide both by their greatest common divisor, which is 10.
• 
• So, the ratio is 15 : 1, which corresponds to option (d).

The ratio of 1 hour to 300 seconds is:

• To compare time, we should convert both times to the same unit. Let's convert 1 hour to seconds (since 1 hour = 3600 seconds).
• 1 hour = 1 × 3600 seconds = 3600 seconds
• Now we have 3600 seconds to 300 seconds. The ratio is  3600 : 300.
• To simplify, divide both by their greatest common divisor, which is 300.
• 
• So, the ratio is 12 : 1, which corresponds to option (b).

In 4 : 7 : : 16 : 28, 7 and 16 are called:

• In a proportion, the first and last terms are called the "extreme terms," and the middle terms are called the "middle terms."
• Here, 4 and 28 are the extreme terms, and 7 and 16 are the middle terms.
• So, the answer is (b) middle terms.

First, second, fourth term are in proportion. The third term will also be in proportion.

First : Second::Third : Fourth

First term =16

Second term =24

Fourth term =54

Third term = x

x = 2 × 18

x = 36

If 12, 21, 72, 126 are in proportion, then:

In a proportion, the product of the first and fourth terms is equal to the product of the second and third terms.
So, let's check each option:
(i) 12×21=72×126 → This is not true.
(ii) 12×72=21×126 → This is not true.
(iii) 12×126=21×72 → This is true.
(iv) None of these → We already found a true statement in option (c).

In a proportion, the product of the first and third terms is equal to the product of the second and fourth terms.
Let's check each option:
(i) x:y::z:x → This doesn't follow the pattern of a proportion.
(ii) x:y::y:z → This follows the pattern of a proportion.
(iii) x:y::z:y → This doesn't follow the pattern of a proportion.
(iv)  x:z::y:z → This doesn't follow the pattern of a proportion.
Therefore, the answer is (b).