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Given below are two statements:

Statement (I):

4 boys and 8 girls completed 1/3 of work in 5 days. After that 3 boys and 3 girls increased, and they completed another 1/3 of work in 3 days. If the remaining work is to be completed in 2 days, then the number of girls that should be increased is 32.

Statement (II):

The ratio of time taken by A and C to do a work is 1:2 respectively. B is 166 (2/3)% more efficient than C. Time taken by A to complete 6% of work is 6 days.

Then, the time taken by B and C together to complete the whole work is 54 (6/11) days.

In light of the above statements, choose the most appropriate answer from the options given below.

Solution

✅ Correct Option: 4

Statement I:

Initial configuration:

44 boys + 88 girls = w1w_1 work per day

Complete 13\frac{1}{3} work in 55 days

So: 5w1=135w_1 = \frac{1}{3} ...(1)

Second configuration:

77 boys + 1111 girls = w2w_2 work per day

Complete 13\frac{1}{3} work in 33 days

So: 3w2=133w_2 = \frac{1}{3} ...(2)

Final requirement:

77 boys + (11+32)(11+32) girls = w3w_3 work per day

Need to complete 13\frac{1}{3} work in 22 days

So: 2w3=132w_3 = \frac{1}{3} ...(3)

The proportions don't maintain consistency when solved.

Statement II:

Let's establish relationships:

  • A:C = 1:21:2 means C's efficiency = 22 × A's efficiency
  • B is 16623%166\frac{2}{3}\% more efficient than C means B = 83\frac{8}{3} × C's efficiency
  • A takes 66 days for 6%6\% work, so 100100 days for full work

For B&C together:

  • C does 11 unit work per day
  • B does 83\frac{8}{3} units work per day
  • Together they do 113\frac{11}{3} units per day
  • Time taken = 100×311=54611\frac{100×3}{11} = 54\frac{6}{11} days

This checks out mathematically.

Therefore, Statement I is false but Statement II is true.

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