He travels $20$ km more due to an increase of speed of $4$ km/hr. Hence, with $10$ km/hr, he travels $\frac{\mathrm{20/}}{4}\times 10=$ km.

Frequency of step of A:B:C = 5 : 6 : 7

But in terms of size of step, 6A = 7B = 8C

Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147

Vipin rests for 10 hours a day. As there are 24 hours in a day, the time he walks is 24 – 10 = 14 hours.

Total time taken = 52days X 14 = 728 hours

As distance is directly proportional to time, to cover double the distance he needs double the time.
That is, 2 x 728 hours.

But, as speed is inversely proportional to time and directly proportional to distance, double distance will require double speed.
That is, total time is
2/2 x 728 = 728 hours.

In the new situation, he rests for twice as much that is,
10 x 2 = 20 hours. Therefore he only walks for 24 – 20 = 4 hours.

If the number of days required is x,
4x = 728
x = 728/4
= 182 days

Lets denote the ages of the man and his son as M and S respectively.

One year ago their ages were M – 1 and S – 1 respectively.

So from the first statement, M – 1 = 4 * (S – 1) or

M – 4*S = -3 ← Equation 1

In 6 years time both would be older by 6 years, or M+6 and S+6.

From the second statement,

M + 6 = 2 * (S +6) + 9, or

M – 2*S = 15 ← Equation 2

Subtracting Equation 1 from Equation 2, we get:

M – 2*S – (M – 4*S) = 15 – (-3)

That is, 2*S = 18 , or S = 9. Therefore the Son’s present age is 9.

From Equation 2, M = 15 + 2*S or M = 15 + 18 = 33.

Therefore the Father’s present age is 33.

Suppose that x kg copper is to be added to the 1 kg alloy.

Now, we know that, the 1 kg alloy has 0.7 kg copper.

And, final percentage of copper in alloy is 75%.

(0.7+x)/(1+x)=75/100=3/4(0.7+x)/(1+x)=75/100=3/4

On cross-multiplication,

2.8+4x = 3+3x

x= 0.2

Therefore,

0.2 kg or 200 g copper should be added to make it’s percentage in the alloy 75%.

Ratio of boys is to girl = 4:5.

Total number of boys = 4x

Total number or girls = 5x

Total number of students : 4x+5x= 9x

9x= 54, x=6.

Total number of boys = 4x = 4×6=24.

It is 3:2 I feel because on adding all the ratios only 3:2 results in 5 i.e 3+2=5 and 5 is not a factor of 12

Or

Here your first option is 2:1

Now splitting 12 in the Ratio 2:1 we get 8 and 4. So, it is possible.

Next you have 3:1 this is also possible ratio as it can be 9 and 3.

Now if we look at 3:2 then it is obviously not possible to split 12 into ratio of 3 and 2.

But still for last one we have7:5 this makes a total of 12. So 7 broken and 5 unbroken is also possible.

So, the correct answer is 3:2.

if u assume x and y and solving u will be annoyed.

Provided 1/4 is the saving, 3/4 is the expenditure

so Expenditure=3, Income = 4

first make A’s Income and Expenditure ratio parts as below

A

7*8 9*7 12*7

8*7 9*7 15*7

Now make first one as 4 parts by multiplying 4 and second make 3 parts by multiplying 3

A’s Income = 7*8*4 = 224

A’s Expenditure = 8*7*3=168 Saving = 56

Now

B’s Income = 9*8*4 = 288

B’s Expenditure = 9*7*3=189 Saving = 99

A’s Income = 12*8*4 = 384

B’s Expenditure = 15*7*3=315 so Saving = 69

Ratio 56:99:69.

Given,
cone,hemisphere and cylinder have same base and equal height.

curved surface area of cone=πrl
curved surface area of cylinder=2πrh
curved surface area of hemisphere=2πr²

ratio=CSA of cone: CSA of hemisphere:CSA of cylinder
=πrl:2πrh:2πr²
=l:2h:2r

Given cost of 5 apples and 4 pears = cost of 7 pears and 3 apples
5A + 4P = 7P + 3A
2A=3P
A/P = 3/2
A:P = 3:2

Hence ratio of cost of 1 apple to 1 pear = 3 : 2

Let the numbers be 3x, 4x

Given, their sum of their squares is 625

→ 9x²+16x²=625

25x²=625

x²=25

x=±5

So, the two numbers are ±15,±20