JIPMAT 2023 (QA) - <p>Given below are two statements:</p> <p>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.</p><p> (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.</p><p>Then, the time taken by B and C together to complete the whole work is 54 (6/11) days.</p><p>In light of the above statements, choose the most appropriate answer from the options given below.</p> | PYQs + Solutions | AfterBoards
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JIPMAT 2023

Arithmetic
>
Time & Work

Medium

Given below are two statements:

Statement (I): \newline 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):\newline 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.

Correct Option: 4
Statement I:
Initial configuration:\newline44 boys + 88 girls = w1w_1 work per day\newlineComplete 13\frac{1}{3} work in 55 days
So: 5w1=135w_1 = \frac{1}{3} ...(1)
Second configuration:\newline77 boys + 1111 girls = w2w_2 work per day\newlineComplete 13\frac{1}{3} work in 33 days
So: 3w2=133w_2 = \frac{1}{3} ...(2)
Final requirement:\newline77 boys + (11+32)(11+32) girls = w3w_3 work per day\newlineNeed 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:\newline- A:C = 1:21:2 means C's efficiency = 22 × A's efficiency\newline- B is 16623%166\frac{2}{3}\% more efficient than C means B = 83\frac{8}{3} × C's efficiency\newline- A takes 66 days for 6%6\% work, so 100100 days for full work
For B&C together:\newline- C does 11 unit work per day\newline- B does 83\frac{8}{3} units work per day\newline- Together they do 113\frac{11}{3} units per day\newline- 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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