Ratio and Proportion Test - 6

Let present ages oftwo persons be 5x and 7x

Given ages of twopersons are in the ratio 5: 7

And also given that18 years ago their ages were in the ratio 8: 13

Therefore (5x –18)/ (7x – 18) = (8/13)

13 (5x – 18) = 8(7x – 18)

65x – 234 = 56x –144

65x – 56x = 234 –144

9x = 90

x = 90/9

x = 10

Thus the ages are5x = 5 (10) = 50 years

And 7x = 7 (10) = 70 years

One score contains20 pencils

And cost per score= 160

Therefore pencilcost = 160/20

= Rs. 8

Cost of one dozenball pen = 84

1 dozen = 12

Therefore cost ofpen = 84/12

= Rs 7

Ratio of the priceof pencil to that of ball pen

= 8/7

= 8: 7

Given two numbersare in the ratio=14:49= 2: 7

And their sum = 81

Sum of terms in theratio = 2 + 7 = 9

First number =(2/9) × 81

= 2 × 9

= 18

Second number =(7/9) × 81

= 7 × 9

= 63

Given that threenumbers are in the ratio 2: 3: 5 and sum of them is 800

Therefore sum ofthe terms of the ratio = 2 + 3 + 5 = 10

First number =(2/10) × 800

= 2 × 80

= 160

Second number =(3/10) × 800

= 3 × 80

= 240

Third number =(5/10) × 800

= 5 × 80

= 400

The three numbers are 160,240 and 400

Given ratio = 7: 8

Let the ratio ofconsequent and antecedent 7x: 8x

Consequent = 80

8x = 80

x = 80/8

x = 10

Antecedent = 7x = 7 × 10 = 70

Given that boys andthe girls in a school are in the ratio 5:4

Sum of the terms ofthe ratio = 5 + 4 = 9

Total strength = 450

Boys strength = (5/9) × 450

= 5 × 50

= 250

Girls strength =(4/9) × 450

= 4 × 50

= 200

Ratio is =49:77=7:11

Let the requirednumbers be 7x and 11x

If 7 is added toeach of them then

(7x + 7)/ (11x + 7)= (2/3)

3 (7x + 7) = 2 (11x+ 7)

21x + 21 = 22x + 14

22x – 21x = 21 – 14

x = 21 – 14 = 7

Thus the numbersare 7x = 7 (7) =49

And 11x = 11 (7) =77

Given that ratio ofzinc and copper in an alloy is 7: 9

Let their ratio =7x: 9x

Weight of copper = 9.0 kg

9x = 9

x = 9/9

x = 1

Weight of the zincin the alloy = 1 × 7

= 7.0kg

Given sides of atriangle are in the ratio 1: 2: 3

Perimeter = 60 cm

Sum of the terms ofthe ratio = 1 + 2 + 3 = 60

First side = (1/6)× 60

= 10 cm

Second side = (2/6)× 60

= 2 × 10

= 20 cm

Third side = (3/6)× 60

= 10 × 3

= 30 cm

Given total amountis to be divided = 270

Ratio 2: 7

The sum of terms =2 + 7

= 9

First ratio ofamount = (2/9) × 270

= 2 × 30

= Rs. 60

Second ratio ofamount = (7/9) × 270

= 7 × 30

= Rs. 210

Given, total numberof students = 36

One out of 6student fails

x out of 36 students

1/6 = x/36

x = 36/6

x = 6

Number of studentswho fail = 6 students

No of students whopass =Total students – Number of students who fail

= 36-6

= 30 students.

Given total amountto be divided = 270

Sum of the terms ofthe ratio = 2 + 3 = 5

Ravish share ofmoney = (2/5) × 270

= 108

And Shikha’s shareof money = (3/5) × 270

= Rs. 162

Given that theratio of income and savings is 7: 2

Let the savings be2x

2x = 200

So, x = 100

Therefore,

Income = 7x

Income = 7 × 100 = 700

Expenditure =Income – savings

= 700 – 200

= Rs.500

Given total amountto be divided = 550

Sum of the terms ofthe ratio = 7 + 4 = 11

Raman’s share ofmoney = (7/11) × 550

= 7 × 50

= Rs. 350

And Aman’s share ofmoney = (4/11) × 550

= 3 × 50

= Rs. 150

Given total amountto be divided = 200

Sum of the terms ofthe ratio = 2 + 3 + 5 = 10

P’s share of money= (2/10) × 200

= 2 × 20

= Rs. 40

And Q’s share ofmoney = (3/10) × 200

= 3 × 20

= Rs. 60

And R’s share ofmoney = (5/10) × 200

= 5 × 20

= Rs. 100