Rajan runs a typing company that processes the manuscript obtained from publishing companies. There are two processes in his work - typing and typesetting. He owns a team each for the two processes. He received a manuscript from a publishing company RBC. He knows that his team of 25 typists can type 225 pages in a day. Also, his team of 7 typesetters can typeset 90 pages in 5 days.
(1) If the manuscript from RBC needs 1350 pages to be typed, how many days will Rajan's team take to type it ?
5
6
7
9
(2) If Rajan employs 5 more typists in his team, in how many days can the work of RBC be completed ?
4
5
6
8
(3) In how many days will Rajan’s team of typesetters typeset the work from RBC ?
50
60
75
85
(4) If typesetting work begins only after the typing work is finished, what is the least number of days Rajan needs to get the work from RBC done by his existing team of 30 typists and 7 typesetters ?
75
80
81
85
Unitary Method
1 Like

Question

Rajan runs a typing company that processes the manuscript obtained from publishing companies. There are two processes in his work - typing and typesetting. He owns a team each for the two processes. He received a manuscript from a publishing company RBC. He knows that his team of 25 typists can type 225 pages in a day. Also, his team of 7 typesetters can typeset 90 pages in 5 days.
(1) If the manuscript from RBC needs 1350 pages to be typed, how many days will Rajan's team take to type it ?
5
6
7
9
(2) If Rajan employs 5 more typists in his team, in how many days can the work of RBC be completed ?
4
5
6
8
(3) In how many days will Rajan’s team of typesetters typeset the work from RBC ?
50
60
75
85
(4) If typesetting work begins only after the typing work is finished, what is the least number of days Rajan needs to get the work from RBC done by his existing team of 30 typists and 7 typesetters ?
75
80
81
85

1 Like

KnowledgeBoat · Accepted Answer

(1) Given:

Number of typists = 25

Pages typed in 1 day = 225

Total manuscript pages to be typed = 1350

Days taken to type 1350 pages = $\dfrac{\text{Total pages}}{\text{Pages typed in 1 day}}$

Substituting the values in above, we get:

Days taken to type 1350 pages = $\dfrac{1350}{225}$

Days taken to type 1350 pages = 6 days

Hence, option 2 is the correct option.

(2) Given:

Original typists = 25

New typists added = 5

Total typists = 25 + 5 = 30

Typing rate of 25 typists = 225 pages per day

Rate of 1 typist = $\dfrac{225}{25} = 9$ pages per day

Rate of 30 typists = 30 x 9 = 270 pages per day

Days taken for 1350 pages = $\dfrac{\text{Total pages}}{\text{Pages typed in 1 day}}$

Substituting the values in above, we get:

Days taken for 1350 pages = $\dfrac{1350}{270}$

Days taken for 1350 pages = 5 days

Hence, option 2 is the correct option.

(3) Given:

Number of typesetters = 7

Pages typeset = 90

Time taken = 5 days

Total manuscript pages = 1350

Pages typeset by 7 typesetters in 1 day = $\dfrac{90}{5}$ = 18 pages

Days taken for 1350 pages = $\dfrac{\text{Total pages}}{\text{Pages typeset in 1 day}}$

Substituting the values in above, we get:

Days taken for 1350 pages = $\dfrac{1350}{18}$

Days taken for 1350 pages = 75 days

Hence, option 3 is the correct option.

(4) Given:

Time taken by 30 typists = 5 days $\quad$ [From step 2]

Time taken by 7 typesetters = 75 days $\quad$ [From step 3]

Condition: Typesetting starts after typing finishes.

Total days = Typing days + Typesetting days

= 5 + 75

= 80 days

Hence, option 2 is the correct option.