Explanation

The solution in the image explains the pattern clearly. Let's break it down:

1. Step 1: Identify the pattern.

   • Difference between 466 and 341 = 125

2. Step 2: Multiply the difference by 2.

   • $125\times 2=250$

   • So, 250 is the correct number inside the parentheses after 341.

3. Step 3: Apply the same pattern to find the missing number.

   • Difference between 398 and 282 = 116

4. Step 4: Multiply the difference by 2.

   • $116\times 2=232$

   • So, the missing number in the sequence is 232.

Explanation

Profit = Selling price - Cost price = 600 - 400 = 200
Profit percentage = $\frac{\mathrm{<font\; color="\#0000ff">200</font>}}{\mathrm{<font\; color="\#0000ff">400</font>}}<font\; color="\#0000ff">\times </font>\mathrm{<font\; color="\#0000ff">100</font>}<font\; color="\#0000ff">=</font>\mathrm{<font\; color="\#0000ff"><span\; style="background-color:\; rgb(255,\; 255,\; 0);">50</span></font>}\mathrm{<font\; color="\#0000ff"><span\; style="background-color:\; rgb(255,\; 255,\; 0);">\%</span></font><span\; class="base"\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><br></span>}$

Explanation

Total work = 16 men × 10 days = 160 man-days
Time for 8 men = $frac{160}{8}$ = 20 days

Explanation

1 carton = 10 boxes × 12 cubes = 120 cubes
Total cartons needed = $\frac{\mathrm{<font\; color="\#ff0000">960</font>}}{\mathrm{<font\; color="\#ff0000">120</font>}}<font\; color="\#ff0000">=</font>\mathrm{<font\; color="\#ff0000">8</font><span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><br></span>}$

Explanation

Let income be $x$.
10% of $x$ = 1500
10/10​0×x=1500
$x=\frac{1500\times 100}{10}<br>$

​=15000

Explanation

Work done by 12 men in 4 days = 1 (full work)

Work done by 1 man in 4 days = 1/12

Work done by 6 men in 4 days = 6/12 = 1/2 (i.e., half of the work)

Work done by 6 men in 2 days = (1/2) × (2/4) = 1/4

Remaining work = 1 - 1/4 = 3/4

15 women complete the full work in 4 days → 1 woman’s 1-day work = 1/(15 × 4) = 1/60

Work needed in 3 days → x women × 3 × (1/60) = 3/4

x = (3/4) × (60/3) = 15 women

Explanation

Work done by 10 women in 7 days = 1

Work done by 1 woman in 7 days = 1/10

Work done by 1 woman in 1 day = 1/(10 × 7) = 1/70

Work done by 10 children in 14 days = 1

Work done by 1 child in 14 days = 1/10

Work done by 1 child in 1 day = 1/(10 × 14) = 1/140

Work done by 5 women in 1 day = 5 × 1/70 = 5/70 = 1/14

Work done by 10 children in 1 day = 10 × 1/140 = 10/140 = 1/14

Total work done per day = 1/14 + 1/14 = 2/14 = 1/7

Total days required = 7 days

Explanation

Step 1: Work Done by A and B Together

• A’s 1-day work = 1/10
• B’s 1-day work = 1/15
• A and B’s 1-day work together:
  1/10​+1/15​=3/30​+2​/30=5/30​=1/6​
• Work done by A and B in 5 days:
  5×1​/6=5/6​

Step 2: Work Left for C

• Total work = 1
• Work remaining after A and B worked for 5 days: $$1 - frac{5}{6} = frac{1}{6}$$
• C completes the remaining 1/6 of the work in 2 days, so C’s 1-day work:
  1/6​÷2=1/12​

Step 3: Wages Calculation

• Total amount = Rs. 1500

• Work done ratio:

  • A's total work = $frac{5}{10} = frac{1}{2}$
  • B's total work = $frac{5}{15} = frac{1}{3}$
  • C's total work = $frac{2}{12} = frac{1}{6}$

• Share of wages:

  • A's share = $frac{1}{2} times 1500 = 750$
    
  • B's share = $frac{1}{3} times 1500 = 500$
    
  • C's share = $frac{1}{6} times 1500 = 250$
    

• Daily wages:

  • B worked 5 days, so B’s daily wage = 500/5 = Rs. 100
  • C worked 2 days, so C’s daily wage = 250/2 = Rs. 125
  • 100+125 = 225

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:

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