Three girl's Sadaf, Iqra and Aadhila to participate in quiz competition based on a book. Sadaf read one - third of the book. Iqra two - fifth and Aadhila read one - fourth. If two pages are still unread. Find the number of pages in the book. How many did each read?
Answers
• Sadaf read one - third of the book.
• Iqra reads two - fifth of the book.
• Aadhila reads one - fourth of the book .
• Pages left unread = 2
The number of pages in the book
⟹ Let the number of pages in book be x
Therefore,
⟹ Number of pages read by Sadaf = 1/3 of x
Number of pages read by Sadaf = 1/3 × x
Number of pages read by Sadaf = x/ 3
⟹ Number of pages by Iqra = 2/5 of x
Number of pages by Iqra = 2/5 × x
Number of pages by Iqra = 2x/5
⟹ Number of pages read by Aadhila = 1/4 of x
Number of pages read by Aadhila = 1/4 × x
Number of pages read by Aadhila = x/4
So
⟹ Number of pages read by Sadaf = x/ 3
Put x as 120
Number of pages read by Sadaf = 120/ 3
Number of pages read by Sadaf = 40
⟹ Number of pages by Iqra = 2x/5
Put x as 120
Number of pages by Iqra = 2× 120/5
Number of pages by Iqra = 2× 24
Number of pages by Iqra = 48
⟹ Number of pages read by Aadhila = x/4
Put x as 120
Number of pages read by Aadhila = 120/4
Number of pages read by Aadhila = 30
Let's verify :-
120 - 40 - 48 - 30 = 2
2= 2
Hence verified
NOTE :-
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Step-by-step explanation:
Verified by Toppr
The funds collected by the schools can be obtained by matrix multiplication:
⎣⎢⎢⎡402535504050203040⎦⎥⎥⎤⎣⎢⎢⎡2510050⎦⎥⎥⎤=⎣⎢⎢⎡700061257875⎦⎥⎥⎤.
funds collected by school A =7000
funds collected by school B =6125
funds collected by school C =7875
Total funds collected =7000+6125+o=21000
★\: \: \sf\bold{\green{Given :-}}★Given:−
• Sadaf read one - third of the book.
• Iqra reads two - fifth of the book.
• Aadhila reads one - fourth of the book .
• Pages left unread = 2
★\: \: \sf\bold{\green{ To \: find \: :-}}★Tofind:−
The number of pages in the book
★\: \: \sf\bold{\green{ Solution\: :-}}★Solution:−
⟹ Let the number of pages in book be x
Therefore,
⟹ Number of pages read by Sadaf = 1/3 of x
Number of pages read by Sadaf = 1/3 × x
Number of pages read by Sadaf = x/ 3
⟹ Number of pages by Iqra = 2/5 of x
Number of pages by Iqra = 2/5 × x
Number of pages by Iqra = 2x/5
⟹ Number of pages read by Aadhila = 1/4 of x
Number of pages read by Aadhila = 1/4 × x
Number of pages read by Aadhila = x/4
⟹\sf\ \: But \: pages \: left \: unread \: = \:\sf\bold{\purple{ 2 }}⟹ Butpagesleftunread=2
So
\begin{gathered}\sf\: \: Total \: number \: of \: pages \: in \: book -Number \: of \: pages \: read \: by \: \:\sf\bold{\red{ Sadaf}} \\ - \sf\:Number \: of \: pages \: read \: by \:\sf\bold{\pink{ Iqra \: }} - \: \sf\:Number \: of \: pages \: read \: by \:\sf\bold{\purple{ Aadhila \: }} = 2\end{gathered}Totalnumberofpagesinbook−NumberofpagesreadbySadaf−NumberofpagesreadbyIqra−NumberofpagesreadbyAadhila=2
⟹x - \frac{x}{3} - \frac{2x}{5} - \frac{x}{4} = 2⟹x−3x−52x−4x=2
⟹ \: \frac{60x - 20x - 24x - 15x}{60} = 2 \: \: \: [ By \: L.C.M]⟹6060x−20x−24x−15x=2[ByL.C.M]
⟹ \frac{1x}{60} = 2⟹601x=2
⟹ x = \frac{2 \times 60}{1}⟹x=12×60
⟹ x = 120⟹x=120
⟹ Number of pages read by Sadaf = x/ 3
Put x as 120
Number of pages read by Sadaf = 120/ 3
Number of pages read by Sadaf = 40
⟹ Number of pages by Iqra = 2x/5
Put x as 120
Number of pages by Iqra = 2× 120/5
Number of pages by Iqra = 2× 24
Number of pages by Iqra = 48
⟹ Number of pages read by Aadhila = x/4
Put x as 120
Number of pages read by Aadhila = 120/4
Number of pages read by Aadhila = 30
Let's verify :-
\begin{gathered}\sf\: \: Total \: number \: of \: pages \: in \: book -Number \: of \: pages \: read \: by \: \:\sf\bold{\red{ Sadaf}} \\ - \sf\:Number \: of \: pages \: read \: by \:\sf\bold{\pink{ Iqra \: }} - \: \sf\:Number \: of \: pages \: read \: by \:\sf\bold{\purple{ Aadhila \: }} = 2\end{gathered}Totalnumberofpagesinbook−NumberofpagesreadbySadaf−NumberofpagesreadbyIqra−NumberofpagesreadbyAadhila=2
120 - 40 - 48 - 30 = 2
2= 2
Hence verified
NOTE :-
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