Explanation

The equation |-x| = 0 simplifies to x = 0 since the absolute value of any number is zero only when the number itself is zero.

Therefore, the solution set contains only {0}.

Explanation

Explanation

x: -3 < x < 6

This represents all numbers greater than -3 and less than 6.

Explanation

We are given:

• Speed while going to school = 3 km/hr

• Speed while returning home = 2 km/hr

• Total time for the round trip = 5 hours

Step 1: Let the Distance Be "d" km

• Time taken to go =d/3​ hours

• Time taken to return = d​/2 hours

Since total time is 5 hours,
d/3​+d/2​=5
Step 2: Solve for d
Taking LCM of 3 and 2 = 6,
2d/6​+3d/6​=5
5d/6​=5
5d=30
$$d=6\text{ km}$$

Explanation

Step 1: Work Done by One Man and One Child in One Day

16 men complete the work in 12 days.
Work done by 16 men in 1 day = 1/12

Work done by 1 man in 1 day = 1/12×16=1/192

24 children complete the work in 18 days.

Work done by 24 children in 1 day = 1/18

Work done by 1 child in 1 day = 1/18×24=1432

Step 2: Work Done by 12 Men and 8 Children in One Day

Work done by 12 men in 1 day = 12×1/192=12/192=1/16

Work done by 8 children in 1 day = 8×1/432=8/432=1/54

Total work done per day by 12 men and 8 children = 1/16+1/54

​ Taking LCM (16, 54) = 432, 

27/432+8/432=35/432

 So, work done per day = 35/432

Step 3: Work Done in 8 Days

Work done in 8 days = 8×35/432=280/432

Remaining work = 1−280/432=152/432

Step 4: Work Done After Adding 3 More Children

Work done by 3 children in 1 day = 3×1/432=3/432

New work rate per day = 35/432+3/432=38/432

Remaining days required = 152/432/38/432=4 days

Explanation

We are given:

• 12 men + 16 boys complete the work in 5 days

• 13 men + 24 boys complete the work in 4 days

• We need to find the ratio of the daily work done by a man to that of a boy.

Step 1: Let M be work done by 1 man in 1 day and B be work done by 1 boy in 1 day

5(12M+16B)=1

4(13M+24B)=1

Step 2: Convert to equations

12M+16B=⅕

4(13M + 24B) = 1​

Step 3: Solve for M and B

Multiply first equation by 4:

48M+64B=⅘

Multiply second equation by 5:

65M+120B=5/4

Convert fractions:

4/5=0.8,5/4=1.25

Solving simultaneously:

Using elimination: Multiply (48M + 64B = 0.8) by 5:

240M+320B=4240M + 320B = 4240M+320B=4

Multiply (65M + 120B = 1.25) by 4:

(260M+480B)- (240M + 320B) =5-4

20M + 160 b = 1

Dividing by 20:

M+8B=1/20M 

Substituting M = 2B from Question 69:

2B+8B=1/20

10B=20/1​

 B=1/200B

​ M=2×1/200=2/200=1/100M

Thus, ratio M:B = 2:1.

Explanation

We are given:

• 5 men and 2 boys = 4 times (1 man + 1 boy)

Step 1: Let work capacities be M (man) and B (boy)

• Work done by 5M + 2B = 4 (M + B)
• Expanding: $5M+2B=4M+4B$
• Rearranging: $5M-4M=4B-2B$
• $$M=2B

So, the ratio of a man’s work to a boy’s work = 2:1.

Answer: (b) 2:1

Explanation

We are given:

24 men complete the work in 16 days → 1 man's 1-day work = 1/24×16=1/38432 women complete the work in 24 days → 1 woman's 1-day work = 1/32×24=1/768 

16 men and 16 women work for 12 days

Step 1: Work done by 16 men and 16 women in 12 days

Work done by 16 men in 1 day = 16×1/384=16/384=1/24

Work done by 16 women in 1 day = 16×1/768=16/768=1/48

Total work done in 1 day = 1/24+1/48=2/48+1/48=3/48=1/16

Total work done in 12 days = 12×1/16=12/16=¾

Step 2: Work remaining

Total work = 1

Work done = ¾

Work remaining = 1−3/4=1/4

Step 3: Additional men required

The remaining work must be completed in 2 days.

Let x be the number of additional men needed.

Work done by (16 + x) men in 1 day = (16+x)×1384(16 + x) 

Work done in 2 days = 2×(16+x)×1384=142

Solving for x:

(16+x)×2/384=¼

16+x=1/4×384/2=384/8=48

x=48−16=32

The closest option is 36 men

Explanation

Since it's a square garden, all sides are equal. To find the length of one side, take the square root of the area:

√2704 m² = 52 m

Explanation

To subtract (-4) from (-6), change the subtraction to addition by changing the sign of the number being subtracted:

-6 - (-4) = -6 + 4

= -2