What number must be subtracted from each term of the ratio 15 23 so that the ratio becomes 7:15

• Textbook Solutions
• Class 7
• Math
• ratio and proportion

Rs Aggarwal 2017 Solutions for Class 7 Math Chapter 8 Ratio And Proportion are provided here with simple step-by-step explanations. These solutions for Ratio And Proportion are extremely popular among Class 7 students for Math Ratio And Proportion Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 7 Math Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 124:

Answer:

[i] HCF of 24 and 40 is 8.
∴ 24 : 40 = 2440= 24 ÷ 840 ÷  8= 35 = 3 : 5

Hence, 24 : 40 in its simplest form is 3 : 5.

[ii] HCF of 13.5 and 15 is 1.5.

 13.515=135150The HCF of  135 and 150 is 15.=135 ÷ 15150 ÷ 15=910

Hence, 13.5 : 15 in its simplest form is 9 : 10.

[iii]  203 : 152=40 : 45
The HCF of 40 and 45 is 5.

∴ 40 : 45 = 4045=40 ÷ 545 ÷  5=89  = 8 : 9

Hence, 623 : 712 in its simplest form is 8 : 9

[iv] 9 : 6
The HCF of 9 and 6 is 3.

[vi] 2.5 : 6.5 : 8 = 25 : 65 : 80

The HCF of 25, 65 and 80 is 5.
∴ 25 : 65 : 80 = 256580= 25 ÷ 565 ÷ 580 ÷ 5 =51316 = 5 : 13 : 16

Page No 124:

Answer:

[i] Converting both the quantities into the same unit, we have:
   75 paise : [3 × 100] paise = 75 : 300

= 75300 = 75 ÷ 75300 ÷ 75=14    [∵ HCF of 75 and 300 = 75]
= 1 paise : 4 paise

[ii]  Converting both the quantities into the same unit, we have:
105 cm : 63 cm = 10563 =105÷2163÷21= 53   [∵ HCF of 105 and 63 = 21]
= 5 cm : 3 cm

[iii] Converting both the quantities into the same unit
65 min : 45 min = 6545= 65÷5 45÷5=139  [∵ HCF of 65 and 45 = 5]
= 13 min : 9 min

[iv] Converting both the quantities into the same unit, we get:
8 months : 12 months = 812=8÷412÷4=23   [∵ HCF of 8 and 12 = 4]
= 2 months : 3 months

[v] Converting both the quantities into the same unit, we get:

2250g : 3000 g = 22503000=2250÷7503000÷750= 34    [∵ HCF of 2250 and 3000 = 750]

= 3 g : 4 g

[vi]  Converting both the quantities into the same unit, we get:
1000 m : 750 m =  1000750=1000÷250750÷250 = 43    [∵ HCF of 1000 and 750 = 250]
= 4 m : 3 m

Page No 124:

Answer:

AB  = 75 and  BC = 914

Therefore, we have:

A B×BC = 75×914AC = 910

∴ A : C = 9 : 10

Page No 124:

Answer:

AB=58 and BC = 1625Now, we have: AB×BC = 58×1625 ⇒AC = 25

∴ A : C = 2 : 5

Page No 124:

Answer:

A : B = 3 : 5

B : C = 10 : 13 =  10÷213÷2=5 :132

Now, A : B : C = 3 : 5 : 132

∴ A : B : C = 6 : 10 : 13

Page No 124:

Answer:

We have the following:

A : B = 5 : 6
B : C = 4 : 7  = 47 = 4×647×64=  6 : 212

∴ A : B : C =  5 : 6 : 212 =  10 : 12 : 21

Page No 124:

Answer:

Sum of the ratio terms  = 7 + 8 = 15

Now, we have the following:

Kunal's share = Rs 360 ×715= 24×7 = Rs 168

Mohit's share = Rs 360 ×815 = 24×8 = Rs 192

Page No 125:

Answer:

Sum of the ratio terms = 15+16=1130

Now, we have the following:
Rajan's share = Rs 880 ×151130 =  Rs 880 ×611 = Rs 80×6  =  Rs 480
Kamal's share = Rs 880 ×161130= Rs  880 ×511= Rs 80 ×5 = Rs 400

Page No 125:

Answer:

Sum of the ratio terms is [1 + 3 + 4] = 8

We have the following:

A's share =  Rs 5600 ×18  =Rs 56008 = Rs 700

B's share =  Rs 5600 ×38= Rs 700 × 3 = Rs 2100

C's share = Rs 5600 ×48 =Rs 700 ×4 = Rs 2800

Page No 125:

Answer:

Let x be the required number.
Then, [9 + x] : [16 + x] = 2 : 3

⇒9+x 16+x = 23⇒27 + 3x  = 32 + 2x ⇒x =5

Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.

Page No 125:

Answer:

Suppose that x is the number that must be subtracted.
Then, [17 − x] : [33 − x] = 7 : 15

⇒17 - x33 - x=715⇒255 -  15x = 231 -  7x ⇒8x =  255 - 231 = 24 ⇒x = 3

Hence, 3 must be subtracted from each term of ratio 17 : 33 so that it becomes 7 : 15.

Page No 125:

Answer:

Suppose that the numbers are 7x and 11x.

Then, [7x + 7] : [11x + 7] = 2 : 3
⇒ 7x + 711x + 7=23

⇒ 21x + 21 = 22x + 14

⇒ x = 7

Hence, the numbers are [7 × 7 =] 49 and [11 × 7 =] 77.

Page No 125:

Answer:

Suppose that the numbers are 5x and 9x.
Then, [5x − 3] : [9x − 3] = 1 : 2

⇒ 5x  - 39x -3=12

⇒ 10x − 6 = 9x− 3
⇒ x = 3

Hence, the numbers are [5 × 3 =] 15 and [9 × 3 =] 27.

Page No 125:

Answer:

Let the numbers be 3x and 4x.
Their LCM is 12x.
Then, 12x = 180
⇒ x = 15

∴ The numbers are [3 × 15 =] 45 and [4 × 15 =] 60.

Page No 125:

Answer:

Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, [8x  + 6] : [3x + 6] = 9 : 4
⇒ 8x+63x+6= 94
⇒ 32x + 24 = 27x + 54
⇒ 5x = 30
⇒ x = 6

Now, present age of A = 8 × 6 yrs = 48 yrs
Present age of  B = 3 × 6 yrs = 18 yrs

Page No 125:

Answer:

Suppose that the weight of zinc is x g.

Then, 48.6 : x = 9 : 5

⇒ x = 48.6×59=2439 = 27

Hence, the weight of zinc in the alloy is 27 g.

Page No 125:

Answer:

Suppose that the number of boys is x.
Then, x : 375 = 8 : 3

⇒ x = 8×3753=8×125 = 1000

Hence, the number of girls in the school is 1000.

Page No 125:

Answer:

Suppose that the monthly income of the family is Rs x.

Then, x : 2500 = 11 : 2

⇒ x = 11×25002=11×1250
⇒ x = Rs 13750

Hence, the income is Rs 13,750.
∴ Expenditure = [monthly income − savings]
                         =Rs [13750 − 2500]
                          = Rs 11250

Page No 125:

Answer:

Let the numbers one rupee, fifty paise and twenty-five paise coins be 5x, 8x and 4x, respectively.

Total value of these coins = [5 x ×100100+ 8x×50100 + 4x ×25100]

 ⇒5x + 8x2  + 4x4= 20x + 16x + 4x4=40x4=10x

However, the total value is Rs 750.
∴ 750 = 10x
⇒ x = 75

Hence, number of one rupee coins = 5 × 75 = 375
Number of fifty paise coins = 8 × 75 = 600
Number of twenty-five paise coins = 4 × 75 = 300

Page No 125:

Answer:

[4x + 5] : [3x + 11] = 13 : 17

⇒4x+ 53x + 11=1317⇒68x + 85 = 39x +  143⇒29x = 58 ⇒x = 2

Page No 125:

Answer:

x y = 34⇒x=3y4

Now, we have [3x + 4y] : [5x + 6y]
=3x +4y 5x + 6y=3×3y4+4y5×3y4+6y= 9y+16y15y +24y  = 25y39y=2539

= 25 : 39

Page No 125:

Answer:

xy = 611⇒x = 6y11

Now, we have:

8x -3y3 x + 2y = 8×6y11 -3y3×6y11+2y =48y-33y18y + 22y =15y40y=38

∴ [8x − 3y] : [3x + 2y] = 3 : 8

Page No 125:

Answer:

Suppose that the numbers are 5x and 7x.
The sum of the numbers is 720.
i.e., 5x + 7x = 720
⇒ 12x= 720
⇒ x = 60

Hence, the numbers are [5 × 60 =] 300 and [7 × 60 =] 420.

Page No 125:

Answer:

[i] The LCM of 6 and 9 is 18.

56=5×36×3=151879 =7×29×2=1418Clearly, 1418