Question

10. What must be added to 2x'y? - 5x+7 to get the sum -5x+y +7x-9
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Answer 1

Answer:

(i) Let the fraction be

y

x

Given,

y−1

x+1

=1

x+1=y−1

x−y=−2 .....(1)

Also,

y+1

x

=

2

1

2x=y+1

2x−y=1 .....(2)

Substracting (1) from (2)

x=3

Substituting value of x in (2),

6−y=1

y=5

Hence, the fraction is

5

3

(ii) Let the age of Nuri be x and that of Sonu be y.

Given,

(x−5)=3(y−5)

3y−x=10 ..... (1)

And,

(x+10)=2(y+10)

2y−x=−10 ....(2)

Subtracting (2) from (1), we get

y=20

Substituting value of y in (1)

60−x=10

x=50

Hence, the ages of Nuri and Sonu are 50 and 20 respectively.

(iii) Let the two digit number be 10x+y

Given, x+y=9 .....(1)

And, 9(10x+y)=2(10y+x)

90x+9y=20y+2x

88x−11y=0 .....(2)

Multiplying (1) by 11, we get

11x+11y=99 ....(3)

Adding (1) and (3)

99x=99

x=1

Substituting this value of x in (1),

1+y=9

y=8

Hence, the number is 18.

(iv) Let the number of Rs 100 notes be x and the number of Rs 50 notes be y.

Given,

x+y=25 ...(1)

And,

100x+50y=2000 ...(2)

Multiplying (1) by 50, we get

50x+50y=1250 ....(3)

Subtracting (3) from (2),

50x=750

x=15

Substituting value of x in (1),

15+y=25

y=10

(v) Let the fixed charge for first 3days be Rsx and after 3days the charge for each day be Rsy.

Given,

x+4y=27 ....(1) [first 3days + 4days]

And,

x+2y=21 ...(2) [first 3days + 2days]

Subtracting (2) from (1), we get

2y=6

y=3

Substituting value of y in (1)

x+4×3=27

x+12=27

x=15

Hence, the fixed charge is Rs 15 and the per day charge is Rs 3.