A Shopkeeper buys a number of books for Rs.80. If he had bought four more books for the same amount,

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30 Jul 2013 Problem

A Shopkeeper buys a number of books for Rs.80. If he had bought four more books for the same amount, each book would have cost him Rs.1 less. How many books did he buy?

OPtion

1) 12
2) 15
3) 16
4) 20
5) 21
6) 24
7) 26
8) 28
9) 32
10)None of these

Solution

Let the number of books purchased for Rs.80 = x
Then cost of each books = 80/x
If he buys for more books, the number of books = x+4
Cost of each book = 80/x+4
(80/x)-[80/(x+4)]=1
Solve x=-20 and x = 16
Rejecting x = -20
The number of books purchased = 16
option 3

Correct Option: 3 Best Solution (26)

Pradyumna K S   11 years AGO

Let the no. of books bought by the shopkeeper be x.

Price of x books = Rs. 80 => Price of 1 book = rs 80/x ...........(i)

Now, if the no. of books had been (x+4)

Price of x+4 books = Rs. 80 => Price of 1 book = Rs 80/ (x+4)...............(ii)

Now, according to the question, (i) - (ii) = 1

i.e 80/x - 80/ (x+4) = 1 => 320/(x2 +4x) = 1

=> x2 +4x - 320 = 0

=> x2 +20x -16x -320 = 0

=> x (x+20) -16 (x+20) = 0

=> (x-16) (x+20) = 0

=> x= 16 or x= -20. But number of books can never be -ve.

Therefore number of books he bought = 16
option 3

Like? Yes (78) | No (21)  

Kalidindi Mounika   11 years AGO

Let the no. of books bought by the shopkeeper be x.
Price of x books = Rs. 80
=> Price of 1 book = rs 80/x ...........(i)
Now, if the no. of books had been (x+4)
Price of x+4 books = Rs. 80
=> Price of 1 book = Rs 80/ (x+4)........(ii)
From the question, (i) - (ii) = 1
=> 80/x - 80/ (x+4) = 1
By solving we'll get
=> (x-16) (x+20) = 0
=> x= 16 or x= -20.
But number of books can never be -ve.
So, number of books he bought = 16

Like? Yes (33) | No (14)  

Deepak Sharma   11 years AGO

Let no. of books is x.
then intial price will be 80/x.
then according to question

(x+4)(80/x-1)=80
x^2+4x-320=0
by solving this quadratic equation
x=16
so 3 option is correct

Like? Yes (24) | No (8)  

Aditya Metkar   11 years AGO

Let shopkeeper bought \'x\' no. of books.
Cost of x books = Rs. 80
so cost of 1 book= 80/x
Now if he had bought 4 more books for Rs. 80 then
cost of each book = 80/(x+4)
By condition given,
(80/x)-(80/(x+4))= 1
Solving x= 16 and -20
As no. of books can not be negative so answer is 16.
Shopkeeper bought 16 books.

Like? Yes (20) | No (5)  

mohan lal garg   11 years AGO

Let the no. of books bought by the shopkeeper be x.

Price of x books = Rs. 80 => Price of 1 book = rs 80/x ...........(i)

Now, if the no. of books had been (x+4)

Price of x+4 books = Rs. 80 => Price of 1 book = Rs 80/ (x+4)...............(ii)

Now, according to the question, (i) - (ii) = 1

i.e 80/x - 80/ (x+4) = 1 => 320/(x2 +4x) = 1

=> x2 +4x - 320 = 0

=> x2 +20x -16x -320 = 0

=> x (x+20) -16 (x+20) = 0

=> (x-16) (x+20) = 0

=> x= 16 or x= -20. But number of books can never be -ve.

Therefore number of books he bought = 16

Like? Yes (16) | No (8)  

Umesh sharma   11 years AGO

Lets suppose he bought X books,
so, X books cost = Rs.80
1 book cost = RS (80/X)
IF he had bought 4 more books then,
(X+4) books cost = Rs. 80
1 book cost = Rs. (80/(X+4))
Therefore,
According to the question,
(80/X)-(80/(X+4))=1
=> 80(X+4-X)=X^2 + 4X
=> X^2 + 4X - 320 =0
=> X(X+20) - 16(X+20)=0
=> (X+20)(X-16)=0
So, X can have two values : (16,-20)
-20 is ignored as number of books cannot be negative.
Thus the answer is 16.

Like? Yes (14) | No (8)  

vishwanand   11 years AGO

let the no. of books be x
cost of one book = 80/x
cost of one book after no. of books increased=80/x+4
so by question we have
80/x-80/x+4=1
by solving this equation we get 16 and -20.
hence no. of books =16.

Like? Yes (13) | No (8)  

Narendra   11 years AGO

Let the no. of books bought by the shopkeeper be x.

Price of x books = Rs. 80 => Price of 1 book = rs 80/x ...........(i)

Now, if the no. of books had been (x+4)

Price of x+4 books = Rs. 80 => Price of 1 book = Rs 80/ (x+4)...............(ii)

Now, according to the question, (i) - (ii) = 1

i.e 80/x - 80/ (x+4) = 1 => 320/(x2 +4x) = 1

=> x2 +4x - 320 = 0

=> x2 +20x -16x -320 = 0

=> x (x+20) -16 (x+20) = 0

=> (x-16) (x+20) = 0

=> x= 16 or x= -20. But number of books can never be -ve.

Therefore number of books he bought = 16

Like? Yes (12) | No (8)  

Girjesh Chandravanshi   11 years AGO

16 book in 80.. cost 5 rs per book
4 more means 20 will cost 4 rs per book.

Like? Yes (11) | No (8)  

krishnapriya   11 years AGO

Let x be the number of books
80/x-80/x+4=1
x^2+4x-320=0
solving the above we get
x=16 or x=-20
therefore,he bought 16 books

Like? Yes (8) | No (6)  

Mahi   11 years AGO

let no.of books be x
so,(80/x)-(80/(x+4))=1
x=16

Like? Yes (10) | No (8)  

FRANKLIN VIJAY   11 years AGO

Let x be the number of books bought.
(80/x -1) * (x+4) = 80
(80 – x) (x+4) / x =80
80x-x^2+320-4x=80x
x^2+4x -320=0
(x+20) (x-16)=0
Since x cannot be negative, x=16

Like? Yes (8) | No (7)  

ABHISHEK KUMAR MISHRA   11 years AGO

let x books previously
then according to question
80/x-1=80/x+4
so x=16

Like? Yes (11) | No (10)  

ravi singh   11 years AGO

let first he buy N books for Rs. 80 then rate of per books is 80/N Rs.,

now second hi buys (N+4) books for Rs. 80 then rate of per books is 80/(N+4) Rs.

now according to the question,

(80/(N+4)) - 1 = 80/N

by solving this we get
N = 16, -20

since no. of books is not a negative no. hence answer is 16

Like? Yes (11) | No (10)  

IFFAT IRAM   11 years AGO

let the number of books bought be x
C.P of x books=80
cost of 1 book = 80/x .....(1)
if he bought x+4 books,
C.P of (x+4) books=80
cost of 1 book=80/(x+4)......(2)
from (1)&(2),
80/x - 80/(x+4)=1
=> 320=x(x+4)
=> x^2+4x-320=0
=> x^2+20x-16x-320=0
=> x(x+20)-16(x+20)=0
=> (x+20)(x-16)=0
=> x=-20 or 16
since no. of books can't be negative
so,
number of books bought is 16
option 3

Like? Yes (10) | No (10)  

Satwiki De   11 years AGO

Trial and error:
80 is Only divisible by 16 and 20 in the list and only 16 satisfies the condition. hence, the answer.

Like? Yes (10) | No (10)  

sachin awachar   11 years AGO

let the no.of books bought by the shopkeeper be n.
price of n books = Rs. 80
Price of 1 book = rs 80/n this is eq.1
if the no. of books had been (n+4)
price of n+4 books will b = Rs. 80
price of 1 book = Rs 80/ (n+4) this is eq.2

ref. 3rd condition we hav
(eq.1) - (eq.2) = 1

i.e 80/n - 80/ (n+4) = 1

320/(n2 +4n) = 1

n2 +4n - 320 = 0

n2 +20n -16n -320 = 0

n (n+20) -16 (n+20) = 0

(n-16) (n+20) = 0

n= 16 or n= -20 taking positive value
therefore number of books he bought = 16

Like? Yes (7) | No (7)  

shivendra pratap singh   11 years AGO

Let x be the number of books bought.
(80/x -1) * (x+4) = 80
(80 – x) (x+4) / x =80
80x-x^2+320-4x=80x
x^2+4x -320=0
(x+20) (x-16)=0
Since x cannot be negative, x=16

Like? Yes (7) | No (7)  

Vinay Sipani    11 years AGO

x --> number of books
y --> Cost of each book

Case 1 => xy = 80 => y = 80/x
Case 2 => (x - 4)(y - 1) = 320

From 1 and 2,
x = 16

Like? Yes (10) | No (11)  

Priyanka Sharma   11 years AGO

suppose he bought n books. then (80/n)-(80/(n+4))=1
solve it to get n=16

Like? Yes (8) | No (9)  

Anil Kumar Bharti   11 years AGO

Exp:
Let no of books=x
80/x - 80/(x+4)=1
x=16 Ans

Like? Yes (6) | No (7)  

divyang   11 years AGO

he bought x books @ 80 rs
and price of 1 book is y rs
so 80=x*y
now if he got 4 more books than the price will be 1 rs less
so if books = x+4 => price/book = y-1
80=(x+4)(y-1)
by try n hit method
we get x=16 and y=5

so he had bought 16 books

Like? Yes (6) | No (7)  

sameer singh   11 years AGO

80/x=y
80/x+4=y-1

Like? Yes (6) | No (8)  

Anilkumar   11 years AGO

80/16=5
80/20=4

Like? Yes (6) | No (8)  

Bingumalla Abinay   11 years AGO

let books be x and price be p
next stage (x+4)(P-1)=px
solving we get x=16

Like? Yes (6) | No (8)  

shekhar pankaj   11 years AGO

There are many lenghty solution ....

Shorcut :
simply if there is increase in book then both the number will be , factor of 80 ..
2*40
4*20
5*16 ..... stop
from last to factors .. we can see when 5 is decreased by 1 then there is increment from 16 to 20
so this will give us answer ... so he had purchased 16 books at rs5 and if he would have purchased 20 books cost would have been 4

Like? Yes (10) | No (12)