Q. 1 A fraction becomes 4/5, if 1 is added to both numerator and denominator. If, however, 5 is
subtracted from both numerator and denominator, the fraction becomes 72. What is the fraction?
Q.2 On selling a TV at 5% gain and a fridge at 10% gain, a shopkeeper gains Rs 2000. But if he sells the
TV at 10% gain and the fridge at 5% loss, he gains Rs 1500 on the transaction. Find the actual prices of
the TV and fridge.
Answers
let the fraction be x/y
1 is added means
x+1/y+1=4/5
5x+5=4y+4
5x-4y=-1
5 is subtracted means
x-5/y-5=1/2
2x-y=5
2 eqn multilply by 5 and 1 eqn by 2
2(5x-4y=-1)=10x-8y=-2
5(2x-y=5)=10x-5y=25
10x-5y=25
10x-8y=-2
x=7,y=9
then the fraction is 7/9
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Solution :-
Let the actual price of the TV be Rs. 'x' and of the fridge be Rs. 'y'.
Situation -1
By selling the TV at 5 % gain and fridge at 10 % gain, the shopkeeper gains Rs. 2000.
⇒ 5x/100 + 10y/100 = 2000
⇒ x/20 + y/10 = 2000/1
Taking the L.C.M. of the denominator and then solving it, we get.
⇒ (x + 2y)/20 = 2000
⇒ x + 2y = 40000 ...........................(1)
Situation - 2
By selling the TV at 10 % gain and fridge at 5 % loss, the shopkeeper gains Rs. 1500. The loss is indicated with the negative sign.
⇒ 10x/100 - 5y/100 = 1500
⇒ x/10 - y/20 = 1500/1
Taking the L.C.M. of the denominator and then solving it, we get.
⇒ (2x - y)/20 = 1500
⇒ 2x - y = 30000 ........................(2)
Now, multiplying the (1) by 2, and then subtracting 2 from it, we get.
First Multiplying (1) by 2 = 2*[(x + 2y) = 40000]
⇒ 2x + 4y = 80000
Now, subtracting (2) from the above.
2x + 4y = 80000
2x - y = 30000
- + -
________________
5y = 50000
__________________
⇒ 5y = 50000
⇒ y = 50000/5
⇒ y = 10000
The actual price of fridge is Rs. 10000.
Now putting the value of y = 10000 in (1), we get.
⇒ x + 2y = 40000
⇒ x + (2*10000) = 40000
⇒ x = 40000 - 20000
⇒ x = 20000
Hence, the actual price of TV is Rs. 20000 and actual price of fridge is Rs. 10000.
Answer.
Answer:
Let the fraction be p/q
give that the fraction will become 4/5 if 1 is added to numerator and denominator
so
4/5 =(p+1)/(q+1)
4q+4 = 5p+5
and
(p-5)/(q-5)=1/2
2p-10=q-5
q= 2p-5
SO
4(2p-5) +4 =5p+5
8p-20+4 = 5p+5
3p= 21
p=7
Therefore q=2*7-5
q=9
So the fraction is 7/9
Step-by-step explanation:
Solution :-
Let the actual price of the TV be Rs. 'x' and of the fridge be Rs. 'y'.
Situation -1
By selling the TV at 5 % gain and fridge at 10 % gain, the shopkeeper gains Rs. 2000.
⇒ 5x/100 + 10y/100 = 2000
⇒ x/20 + y/10 = 2000/1
Taking the L.C.M. of the denominator and then solving it, we get.
⇒ (x + 2y)/20 = 2000
⇒ x + 2y = 40000 ...........................(1)
Situation - 2
By selling the TV at 10 % gain and fridge at 5 % loss, the shopkeeper gains Rs. 1500. The loss is indicated with the negative sign.
⇒ 10x/100 - 5y/100 = 1500
⇒ x/10 - y/20 = 1500/1
Taking the L.C.M. of the denominator and then solving it, we get.
⇒ (2x - y)/20 = 1500
⇒ 2x - y = 30000 ........................(2)
Now, multiplying the (1) by 2, and then subtracting 2 from it, we get.
First Multiplying (1) by 2 = 2*[(x + 2y) = 40000]
⇒ 2x + 4y = 80000
Now, subtracting (2) from the above.
2x + 4y = 80000
2x - y = 30000
- + -
________________
5y = 50000
__________________
⇒ 5y = 50000
⇒ y = 50000/5
⇒ y = 10000
The actual price of fridge is Rs. 10000.
Now putting the value of y = 10000 in (1), we get.
⇒ x + 2y = 40000
⇒ x + (2*10000) = 40000
⇒ x = 40000 - 20000
⇒ x = 20000
Hence, the actual price of TV is Rs. 20000 and actual price of fridge is Rs. 10000
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