Ratio of two number is 5: 6 and their HCF is 6. LCM of these two numbers is:

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Ratio of two number is 5: 6 and their HCF is 6. LCM of these two numbers is:

A150

B180

C90

D120

Akhilesh ? Apr 3 '25 at 21:26

correct answer is: 180
Explanation: The ratio of the two numbers is 5:6, so let the numbers be 5k and 6k.

The HCF of these numbers is k. Given that the HCF is 6, we find k=6.

Thus, the numbers are 30 and 36.

Using the formula $\text{LCM(a,b)} = \frac{(a \times b)}{\text{HCF(a,b)}}$,

the LCM is $\frac{(30\times36)}{6}$ = 180.

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The ratio of heights of 2 cones is 3 : 4 and the ratio of radius of 2 cones is 5 : 6. Find the ratio of volumes of 2 cones.

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The ratio of heights of 2 cones is 3 : 4 and the ratio of radius of 2 cones is 5 : 6. Find the ratio of volumes of 2 cones.

A75/144

B75/72

C72/75

D144/75

Akhilesh ? Apr 3 '25 at 20:04

correct answer is: 75/144
Explanation: The volume of a cone is proportional to the square of the radius and the height. Given the ratios of heights (3:4) and radii (5:6), the volume ratio is calculated as (5²/6²) * (3/4) = (25/36)*(3/4) = 75/144.

• OPTION a (75/144): Correct, as shown by the calculation.
• OPTION b (75/72): Incorrect, as it doesn't match the calculated ratio.
• OPTION c (72/75): Incorrect, inverse of the correct ratio.
• OPTION d (144/75): Incorrect, inverse of the correct ratio.

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The ratio of length of 2 trains is 5 : 6 and the ratio of their speeds is 2: 3. Find the ratio of time taken by them to cross a pole.

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The ratio of length of 2 trains is 5 : 6 and the ratio of their speeds is 2: 3. Find the ratio of time taken by them to cross a pole.

A05:04

B07:04

C02:07

D05:07

Akhilesh ? Apr 2 '25 at 23:24

correct answer is: 05:04
Explanation: The ratio of the time taken by the two trains to cross a pole is determined by the ratio of their lengths divided by their respective speeds. For the first train, the time is $\frac{5}{2}$ units, and for the second train, it is $\frac{6}{3} = 2$ units. Simplifying the ratio $\frac{5}{2} : 2$ gives $5:4$

• OPTION a (05:04): Correct, as derived above.
• OPTION b (07:04): Incorrect, as it does not match the calculated ratio.
• OPTION c (02:07): Incorrect, as it inverses the correct ratio.
• OPTION d (05:07): Incorrect, as it does not match the calculated ratio.

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The ratio of water and milk in a mixture of 65 litre is 5 : 8. What quantity of water(in litre) must be added so that the ratio of water and milk becomes 3: 4?

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The ratio of water and milk in a mixture of 65 litre is 5 : 8. What quantity of water(in litre) must be added so that the ratio of water and milk becomes 3: 4?

A3 litres

B4 litres

C5 litres

D6 litres

Akhilesh ? Apr 1 '25 at 20:29

correct answer is: option c [5 litres]
Explanation: Initially, the mixture has 65 litres with a water to milk ratio of 5:8. First, determine the initial quantities of water and milk.
Let the initial quantity of water be $5x$ litres and the initial quantity of milk be $8x$ litres. Therefore, $5x + 8x = 65$.
This simplifies to $13x = 65$, so $x = 5$.
Initial quantity of water = $5 \times 5 = 25$ litres.
Initial quantity of milk = $8 \times 5 = 40$ litres.
Let the quantity of water to be added be $y$ litres. The new quantity of water becomes $25 + y$ litres, while the quantity of milk remains 40 litres.
The new ratio of water to milk is 3:4. Thus, $\frac{25 + y}{40} = \frac{3}{4}$.
Cross-multiplying gives $4(25 + y) = 3 \times 40$, which simplifies to $100 + 4y = 120$.
Therefore, $4y = 20$, and $y = 5$.
So, 5 litres of water must be added

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A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes are equal. What is the total number of notes ?

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A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes are equal. What is the total number of notes ?

A60

B90

C75

D45

Akhilesh ? Mar 18 '25 at 22:54

correct answer is: 90
Explanation: Let the number of each type of note be $n$. The total amount from each type is $1n + 5n + 10n = 16n$. Setting this equal to 480 gives $n = 30$. Thus, the total number of notes is $3 \times 30 = 90$.

• Option a (60): Incorrect, as $16 \times 60 = 960$, which exceeds 480.
• Option b (90): Correct, as explained above.
• Option c (75): Incorrect, as $16 \times 75 = 1200$, which is too high.
• Option d (45): Incorrect, as $16 \times 45 = 720$, which is also too high.

 

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