Ratio and Proportion Test - 7

Given 4 : 5 or 16 : 25

LCM for 5 and 25 is 25

4 : 5 can be written as = 4/5

4/5 × 5/5 = 20/25

And we have 16/25

Clearly 20 > 16

Therefore 4 : 5 > 16 : 25

Given that income =1800

Given the ratio ofincome and expenditure = 9:5

9x = 1800

Therefore x = 200

Expenditure = 5x = 5 × 200 = Rs.1000

Savings = Income –Expenditure

= 1800 -1000

= Rs.800

Given 15: 16 or 24:25

LCM for 16 and 25is 400

15: 16 can bewritten as = 15/16

15/16 × (25/25) =375/400

And we have 24/25

24/25 × (16/16) =384/400

Clearly 384 >375

Therefore 15: 16 > 24:25

Given 8:9 = x: 48

In proportion weknow that product of extremes = product of means

8/9= x/48

On crossmultiplying

x = (8 × 48)/ 9

x = 126/3

Given that the ratioof income of a person to his savings is 5: 1

Savings per year = 7200

Savings per month= 7200/12

= Rs.600

Then let income permonth be x

x: 600 = 5:1

x = 600 × 5

x = 3000

Income per month is Rs. 3000

Given 6: 8

By multiplying bothnumerator and denominator by 2 we equivalent ratios

6/8 × (2/2) = 12/16

And also bydividing both numerator and denominator by 2 we equivalent ratios

(6/2)/ (8/2) = 3/4

Two equivalent ratios are3: 4 = 12: 16

Given 9: 20 or 8:13

LCM for 20 and 13is 260

9: 20 can bewritten as = 9/20

9/20 × (13/13) =117/260

And we have 8/13

8/13 × (20/20) =160/260

Clearly 160 >117

Therefore 9: 20< 8: 13

Given 72, 84, 186,217

Product of extremes= 72 × 217 = 15624

Product of means =84 × 186 = 15624

Therefore productof extremes = product of means

Hence given numbersare in proportion.

Given 33, 44, 66,88

Product of extremes= 33 × 88 = 2904

Product of means =44 × 66 = 2904

Therefore productof extremes = product of means

Hence given numbers are in proportion.

Given x: 87 = 3: 29

In proportion weknow that product of extremes = product of means

x/ 87 = 3/29

On crossmultiplying

x = (87 × 3)/ 29

x = 9

Given that thescale of map = 1: 4000000

Let us assume theactual distance between towns is x cm

1: 4000000 =5: x

x= 5 × 4000000 

x = 20000000 cm

We know that 1km =1000 m

1m = 100 cm

Therefore

x = 200 km

Given 4: 7 or 5: 8

LCM for 7 and 8 is56

4: 7 can be writtenas = 4/7

4/7 × (8/8) = 32/56

And we have 5/8

5/8 × (7/7) = 35/56

Clearly 35 > 32

Therefore 4: 7 <5: 8

12/20 = 3/5

Consider 12/20 = …./5

Let unknown valuebe x

Therefore 12/20 =x/5

On crossmultiplying

x = 60/20

x = 3.

Given 46, 69, 69,46

Product of extremes= 46 × 46 = 2116

Product of means =69 × 69 = 4761

Therefore productof extremes is not equal to product of means

Hence given numbers are notin proportion.

Given 1: 2 or 13:27

LCM for 2 and 27 is54

1: 2 can be writtenas = 1/2

1/2 × (27/27) =27/54

And we have 13/27

13/27 × (2/2) =26/54

Clearly 27 > 26

Therefore 1: 2 > 13: 27