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Rewrite the following sentences as indicated in the brackets: a. Raju never does yoga in the morning. ? (Supply a correct tag) b. Sita speaks English fluently. (Change into 'who' / 'whom' questions) c. He (not complete) his task yet. (Use the verb given in bracket in the correct tense) d. Rita said, "I watched the drama last night." (Reported speech) e. We welcome our guests. (Change into passive voice.)

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6 steps

Let the work rates (fractions of work per day) of the father, mother, son, and daughter be FF, MM, SS, and DD respectively.

  1. Given that father and mother together complete the work in 12 days.

    F+M=112F + M = \frac{1}{12}

  2. Given that son and daughter together complete the work in 15 days.

    S+D=115S + D = \frac{1}{15}

  3. Given that father and son together complete the work in 10 days.

    F+S=110F + S = \frac{1}{10}

  4. Adding the rates from Steps 1 and 2 gives the combined rate of all four.

    (F+M)+(S+D)=112+115(F + M) + (S + D) = \frac{1}{12} + \frac{1}{15}

    Find a common denominator of 60:

    112=560,115=460\frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60} 560+460=960=320\frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20}

    So,

    F+M+S+D=320F + M + S + D = \frac{3}{20}

  5. The combined rate of mother and daughter is the total rate minus the father and son rate from Step 3.

    M+D=(F+M+S+D)−(F+S)=320−110M + D = (F + M + S + D) - (F + S) = \frac{3}{20} - \frac{1}{10}

    Convert 110\frac{1}{10} to twentieths:

    110=220\frac{1}{10} = \frac{2}{20} 320−220=120\frac{3}{20} - \frac{2}{20} = \frac{1}{20}

  6. Time taken by mother and daughter together is the reciprocal of their combined rate.

    Time=1120=20 days\text{Time} = \frac{1}{\frac{1}{20}} = 20 \text{ days}

    20 days

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