Question 14 Marks
Prabhat runs a typing company that processes the manuscripts obtained from publishing companies. There are two processes in this work—typing and typesetting. He owns one team for each of the two processes. He received a manuscript of 3960 pages from a publishing company ABD. He knows that his team of 24 typists can type 264 pages in a day and his team of 6 typesetters can typeset 360 pages in 4 days.
Q.1. How many days will Prabhat's team take to type the manuscript?
(a) 14 days$\quad$(b) 15 days$\quad$(c) 16 days$\quad$(d) 18 days
Q.2. If Prabhat employs 6 more typists in his team, in how many days will he be able to finish the typing work?
(a) $18 \frac{3}{4}$ days$\quad$(b) 15 days$\quad$(c) 12 days$\quad$(d) 10 days
Q.3. In how many days will Prabhat's team of typesetters finish typesetting the work?
(a) 48 days$\quad$ (b) 44 days$\quad$(c) 66 days$\quad$(d) 64 days
Q.4. If typesetting work begins only after the typing work is finished, what is the least number of days Prabhat needs to get the work done with his team of 30 typists and 6 type setters?
(a) 56 days $\quad$(b) 78 days$\quad$(c) 81 days$\quad$(d) 59 days
Q.1. How many days will Prabhat's team take to type the manuscript?
(a) 14 days$\quad$(b) 15 days$\quad$(c) 16 days$\quad$(d) 18 days
Q.2. If Prabhat employs 6 more typists in his team, in how many days will he be able to finish the typing work?
(a) $18 \frac{3}{4}$ days$\quad$(b) 15 days$\quad$(c) 12 days$\quad$(d) 10 days
Q.3. In how many days will Prabhat's team of typesetters finish typesetting the work?
(a) 48 days$\quad$ (b) 44 days$\quad$(c) 66 days$\quad$(d) 64 days
Q.4. If typesetting work begins only after the typing work is finished, what is the least number of days Prabhat needs to get the work done with his team of 30 typists and 6 type setters?
(a) 56 days $\quad$(b) 78 days$\quad$(c) 81 days$\quad$(d) 59 days
Answer
View full question & answer→1. (b): Time needed to type 264 pages $=1$ day.
Time needed to type 1 page $=\frac{1}{264}$ days. [less pages, less days]
$\therefore$ time needed to type 3960 pages $=\frac{3960}{264}=15$ days. [more pages, more days]
So, Prabhat's team will type the manuscript in 15 days.
2. (c): After employing 6 more typists, Prabhat's typing team $=(24+6)=30$ typists.
Time needed by 24 typists to type the manuscript $=15$ days .
Time needed by 1 typist to type the manuscript $=(15 \times 24)$ days. [less men, more days]
$\therefore$ time needed by 30 typists to type the manuscript $=\frac{15 \times 24}{30}=12$ days.
3. (b): Time needed to typeset 360 pages $=4$ days.
Time needed to typeset 1 page $=\frac{4}{360}$ days. [less pages, less days]
$\therefore$ time needed to typeset 3960 pages $=\frac{4}{360} \times 3960=44$ days. [more pages, more days]
4. (a): Total number of days required = 12 + 44 = 56 days.
Time needed to type 1 page $=\frac{1}{264}$ days. [less pages, less days]
$\therefore$ time needed to type 3960 pages $=\frac{3960}{264}=15$ days. [more pages, more days]
So, Prabhat's team will type the manuscript in 15 days.
2. (c): After employing 6 more typists, Prabhat's typing team $=(24+6)=30$ typists.
Time needed by 24 typists to type the manuscript $=15$ days .
Time needed by 1 typist to type the manuscript $=(15 \times 24)$ days. [less men, more days]
$\therefore$ time needed by 30 typists to type the manuscript $=\frac{15 \times 24}{30}=12$ days.
3. (b): Time needed to typeset 360 pages $=4$ days.
Time needed to typeset 1 page $=\frac{4}{360}$ days. [less pages, less days]
$\therefore$ time needed to typeset 3960 pages $=\frac{4}{360} \times 3960=44$ days. [more pages, more days]
4. (a): Total number of days required = 12 + 44 = 56 days.