Explanation

Let the two-digit number be xy, where x is the tens digit and y is the units digit.
The sum of its digits is x + y.
The number is three times the sum of its digits, so we can write an equation: xy = 3(x + y).
Simplify the equation: 10x + y = 3x + 3y.
Rearrange the equation to get: 7x = 2y.
Now, if 45 is added to the number, the digits are reversed, so we can write another equation: xy + 45 = yx.
Simplify the equation: 10x + y + 45 = 10y + x.
Rearrange the equation to get: 9x = 9y - 45.
Divide both sides by 9 to get: x = y - 5.
Now we have two equations:

1. 7x = 2y

2. x = y - 5

Substitute the second equation into the first equation:
7(y - 5) = 2y
Expand and simplify:
7y - 35 = 2y
5y = 35
y = 7
Now that we have found y, substitute it back into one of the original equations to find x:
x = y - 5
x = 7 - 5
x = 2
So, the original number is 27.

Explanation

Waking - 1/3 hours = 20 min

Motorbike ride = 1/2 hours = 30 min

Total journey = 20 + 30 = 50 min

Portion of Bike ride = 30/50 = 0.6

ND16-3-2023

Explanation

Explanation

To solve this, we can start by expressing the given ratio m:n = 3:2 in terms of a variable, let's say x. So, m = 3x and n = 2x.

Now, let's substitute these expressions into the given ratio (4m+5n):(4m-5n):

(4(3x) + 5(2x)) : (4(3x) - 5(2x))

Expanding and simplifying, we get:

(12x + 10x) : (12x - 10x)

22x : 2x

Now, we can divide both terms by 2x to get: 11 : 1

Explanation

21 binders bind 1400 books in 15 days, so 1 binder binds:

1400/21 = 66.67 books in 15 days

= 66.67/15 = 4.44 books per day

To bind 800 books in 20 days, we need:

800/20 = 40 books per day

Number of binders required = 40/4.44 = 9

So, 9 binders are required to bind 800 books in 20 days.

Explanation

To find how many shirts the washerman can iron in one hour (60 minutes), we can use the given rate:

• The washerman irons 4 shirts in 12 minutes.

Now, let's find how many sets of 12 minutes are there in 60 minutes:

60​/12=5

Since he can iron 4 shirts in 12 minutes, in 60 minutes he can iron:

4×5=20 shirts

Explanation

0.005 × 0.2 = 0.001

So, the product of 0.005 and 0.2 is 0.001.

Explanation

A and B can do the work in 12 days, so their combined rate of work is 1/12 of the work per day.

B and C can do the work in 15 days, so their combined rate of work is 1/15 of the work per day.

C and A can do the work in 20 days, so their combined rate of work is 1/20 of the work per day.

Now, let's add the three equations and simplify:

2(A + B + C) = 1/12 + 1/15 + 1/20

Combine like terms:

2(A + B + C) = (10 + 8 + 6) / 120

Simplify the fraction:

2(A + B + C) = 24 / 120

Divide both sides by 2:

A + B + C = 12 / 120

Simplify the fraction:

A + B + C = 1/10

So, A, B, and C together can complete 1/10 of the work in one day.

To find the number of days taken by A, B, and C together to finish the work, we take the reciprocal:

Number of days = 1 / (1/10) = 10 days

Explanation

Sum of the ages of 3 friends =3×23= 69 years

Sum of the ages of 4 friends =4×23= 92 years

∴ Age of 4th friend = 92 years - 69 years = 23 years.

Explanation