Question Detail

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.

Answer: Option D

Explanation:

Let the first number is A and second number is B.

As per question

$\begin{aligned} \frac{40}{100}A = \frac{2}{3}B \\ \frac{A}{B} = \frac{2}{3}*\frac{100}{40} \\ \frac{A}{B} = \frac{5}{3} \\ => A:B = 5:3 \end{aligned}$

1. The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.

20:33:60
21:33:60
22:33:60
23:33:60

Answer: Option D

Explanation:

Let A salary be 2k
B salary be 3k and C salary be 5k

$\begin{aligned} \text{A's new salary = }\frac{115}{100}*2k \\ = \frac{23}{10}k \\ \text{B's new salary = }\frac{110}{100}*3k \\ = \frac{33}{10}k \\ \text{C's new salary = }\frac{120}{100}*5k \\ = 6k \\ \text{New ratio = }\\ \frac{23k}{10}:\frac{33k}{10}:6k \\ = 23:33:60 \\ \end{aligned}$

2. If a:b = 2:3 and b:c = 4:3, then find a:b:c

8:12:9
2:3:8
2:3:9
2:3:12

Answer: Option A

Explanation:

$\begin{aligned} a:b = 2:3 \\ b:c = 4:3 = (4*\frac{3}{4} : 3*\frac{3}{4}) \\ = 3:\frac{9}{4} \\ a:b:c = 2:3:\frac{9}{4} \\ = 8:12:9 \end{aligned}$

3. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D

15:24:30:35
16:24:30:35
17:24:30:35
18:24:30:35

Answer: Option B

Explanation:

$\begin{aligned} A:B = 2:3 \\ B:C = 4:5 = (4*\frac{3}{4} : 5*\frac{3}{4}) \\ = 3:\frac{15}{4} \\ C:D = 6:7 = (6*\frac{15}{24} : 7*\frac{15}{24}) \\ = \frac{15}{4}:\frac{35}{8} \\ A:B:C:D = 2:3:\frac{15}{4}:\frac{35}{8} \\ = 16:24:30:35 = 8:12:9 \end{aligned}$

4. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

Answer: Option C

Explanation:

Let the third number be x.
First Number (120/100)*x = 6x/5
Second Number (150/100)*x = 3x/2

Ratio = 6x/5:3x/2
=> 4:5

5. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

Answer: Option B

Explanation:

Let the numbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒ 38x = 1862
⇒ x = 49 ⇒ x = 7.
middle number = 2x = 14

Question Detail

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.

1. The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.

2. If a:b = 2:3 and b:c = 4:3, then find a:b:c

3. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D

4. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

5. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

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Question Detail

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.

1. The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.

2. If a:b = 2:3 and b:c = 4:3, then find a:b:c

3. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D

4. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

5. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

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