Explanation

Let number of boys are x and then number of girls
= (100 - x)
Thus,
50x + (100 - x) × 40 = 46 × 100
→ x = 60
Number of boys = 60

Explanation

Full tank capacity = Distance ÷ Miles per gallon

= 250 miles ÷ 15 miles/gallon

= 16.67 gallons (approximately)

Now, if the car gets 20 miles per gallon, we can calculate the distance it can travel on a full tank:

Distance = Full tank capacity × Miles per gallon

= 16.67 gallons × 20 miles/gallon

= 333.4 miles

Explanation

To find the number of lawns completed in 10 hours, we can set up a proportion:

2 hours / 3 lawns = 10 hours / x lawns

We can then cross-multiply and solve for x:

2x = 3 × 10

2x = 30

x = 30/2

x = 15

So, in 10 hours, 15 lawns will be completed.

Explanation

To find the smallest ratio, we need to simplify the fraction 0.35/0.65.

First, convert the decimals to fractions:

0.35 = 35/100 = 7/20

0.65 = 65/100 = 13/20

Now, divide the fractions:

(7/20) ÷ (13/20) = 7/13

So, the smallest ratio is 7/13.

Explanation

A and B together can complete the work in 3 days, so their combined rate of work is 1/3 per day.

They work together for 2 days, so they complete 2/3 of the work.

B leaves, and A completes the remaining 1/3 of the work in 2 days. This means A's rate of work is 1/6 per day (since A completes 1/3 of the work in 2 days).

Now, we know B's rate of work is the difference between their combined rate and A's rate: (1/3 - 1/6) = 1/6 per day.

Since B can complete the entire work in x days, B's rate of work is also 1/x per day.

Equating the two expressions for B's rate of work, we get: 1/6 = 1/x --> x = 6

So, B alone can complete the work in 6 days.

Explanation

A is 4 times as fast as B, so A's rate of work is 4 times B's rate of work.

Since A finishes the work in 45 days less than B, let's assume B takes x days to finish the work. Then A takes x - 45 days to finish the work.

Since A is 4 times as fast as B, A's rate of work is 4 times B's rate of work. So, A's time to finish the work is 1/4 of B's time.

We can set up an equation based on the above: x - 45 = (1/4)x

Solve for x: x - 45 = (1/4)x --> 4x - 180 = x --> 3x = 180 --> x = 60

So B takes 60 days to finish the work, and A takes 60 - 45 = 15 days to finish the work.

Since A and B work together, their combined rate of work is the sum of their individual rates. Let's find their individual rates.

B's rate = 1/60 (work done per day)

 A's rate = 1/15 (work done per day)

Combined rate = (1/60 + 1/15) = (1/60 + 4/60) = 5/60 = 1/12

So A and B together can complete the work in 12 days.

Explanation

The sum of angles of a triangle equals the straight angle 180 degrees.

A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

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FIA CBT VU PAPER 17-12-2021

Explanation

In the first y hours, the carpenter lays xy bricks.

In the 2y hours thereafter, he lays (x/2)(2y) = xy bricks.

Altogether, that's xy + xy = 2xy bricks.

Explanation

- The player's average runs in 10 innings is 33, so the total runs scored by the player in 10 innings is:

33 x 10 = 330 runs

- To increase the average by 3, the new average will be:

33 + 3 = 36

- Since the player has already played 10 innings, the total number of innings now becomes 11 (including the next innings).

- Let x be the runs scored in the next innings. The new total runs will be:

330 + x

- The new average is 36, so we can set up the equation:

(330 + x) / 11 = 36

- Solve for x:

330 + x = 396
x = 66
So, the player needs to score 66 runs in the next innings to increase the average by 3.

Explanation

Let the number be x
According to the question,
91 - 

 = x
9100 - 30x = 100x
Or, 9100 = 130x
Or, x = 

Hence, x = 70