Ratio And Proportion Class 8
Ratio And Proportion
Exercise :
Q.1) Express each of the following ratios in simplest form:
i) 18 : 30 = 18
30
= 3
5
ii) 7.5 : 9 = 75 / 10 : 9 = 75/90 = 5 /6
iii) 1 , 1 , 1
6 9 12
LCM of 6 , 9, 12 is 36
1 * 36 , 1 * 36 , 1 * 36
6 9 12
= 6 , 4 , 3
Q 2 . Divide ₹ 142.20 between Gagan and Mukesh in the ratio 1/4 : 1/5
Solution :
Given ratio = 1 : 1
4 5
= 1 * 20 : 1 * 20
4 5
= 5 : 4
Sum of ratio = 5 + 4 = 9
Gagan's Share = 142.20 * 5
9
= 711/9
= 79
Mukesh's Share = 142.20 * 4
9
= 568.8/9
= 63.20
Gagan's Share = ₹ 79 and Mukesh's Share = ₹ 63.20
Q.3) Divide ₹ 3726 among A, B, C in the ratio 1 : 1 : 1
3 4 6
Solution :
Given ratio = 1 : 1 : 1
3 4 6
L.C.M of 3, 4 and 6 is 12
= 1 * 12 : 1 * 12 : 1 * 12
3 4 6
= 4 : 3 : 2
Sum of ratio = 4 + 3 + 2 = 9
A's Share = 3726 * 4
9
= 414 * 4
= 1656
B's Share = 3726 * 3
9
= 414 * 3
= 1242
C's Share = 3726 * 2
9
= 414 * 2
= 828
A's Share = ₹ 1656 , B's Share = ₹ 1242 and C's Share = ₹ 828
Q.4) Divide ₹ 1050 between Geeta and Renu in the ratio 22/3 : 62/3
Solution :
Given ratio = 22/3 : 62/3 = 8 : 20
3 3
= 8 * 3 : 20 * 3
3 3
= 8 : 20
Sum of ratio = 8 + 20 = 28
Geeta's Share = 1050 * 8
28
= 37.5 * 8
= 300
Renu's Share = 1050 * 20
28
= 37.5 * 20
= 750
Geeta's Share = ₹ 300 and Renu's Share = ₹ 750
Q.5) Divide ₹ 747 among ABC such that 4A = 5B = 7C
Solution :
Let 4A = 5B = 7C = K
so,
4A = K ; 5B = K ; 7C = K
A = K ; B = K ; C = K
4 5 7
K : K : K
4 5 7
L.C.M. of 4 ,5 and 7 is 140
K * 140 : K * 140 : K * 140
4 5 7
35 : 28 : 20
Sum of ratio = 35 + 28 + 20
= 83
A's Share = 747 * 35
83
= 9 * 35
= ₹ 315
B's Share = 747 * 28
83
= 9 * 28
= ₹ 252
C's Share = 747 * 20
83
= 9 * 20
= ₹ 180
A's Share = ₹ 315 , B's Share = ₹ 252 and C's Share = ₹ 180
Q.6) A bag contains ₹1, 50p and 25p coins in the ratio 5 : 6 : 8 amounting to ₹ 210. Find the number of coins of each type.
Solution :
Let the number of 1 rupee , 50paise and 25paise coins be 5x , 6x and 8x respectively.
5x + 6x/2 by + 8x/4 = 210
5x + 3x + 2x = 210
10x = 210
x = 21
1 rupee = 5x = 5 * 21 = 105
50paise coins = 6x = 6 * 21 = 126
25paise coins = 8x = 8 * 21 = 168
Q.7) A: B = 2 : 5 and B : C = 7 : 9. Find A : B : C
Solution:
A = 2 ; B = 7
B 5 C 9
A = 2 * 7 ; B = 7 * 5
B 5 * 7 C 9 * 5
A = 14 ; B = 35
B 35 C 45
A : B : C = 14 : 35 : 45
Q. 8) If A : B = 4 : 9 and A : C = 2 : 3, find B : C and A : B : C
Solution:
A = 4 ; A = 2
B 9 C 3
A = 4 ; A = 2 * 2
B 9 C 3 * 2
A = 4 ; A = 4
B 9 C 6
A : B : C = 4 : 9 : 6
B : C = 9 : 6 = 3 : 2
Q. 9) Two numbers are in ratio 6:11. On adding 2 to the first and 7 to the second, their ratio becomes 8:15. Find the numbers.
Solution :
let required numbers be 6x and 11x.
Then,
6x + 2 = 8
11x + 7 15
15 ( 6x + 2) = 8 ( 11x + 7)
90x + 30 = 88x + 56
90x - 88x = 56 - 30
2x = 26
x = 26 / 2
x = 13
Required numbers are 6x = 6 * 13 = 78
11x = 11 * 13 = 143
Q 10) A sum of money is divided between Mohan and Sohan in the ratio 5:7. If Sohan's share is ₹ 665, find the total amount.
Solution :
ratio of sum of money is divided between Mohan and Sohan is 5 : 7
Mohan's Share = 5
Sohan's Share 7
Mohan's Share = 5 * Sohan's share
7
= 5 * 665
7
= 5 * 95
= ₹ 475
Total amount = ₹ 475 + ₹ 665
= ₹ 1140
Q 11) A certain sum of money is divided among in the ratio 5 : 6 : 7. If A's is ₹175, find the total amount and the share of each one of B and C.
Solution : Let total amount be x
Sum of ratio = 5 + 6 + 7 = 18
A' share = x * 5
18
175 = x * 5
18
x = 175 * 18
5
x = 35 *18
x = ₹ 630
Total amount = ₹ 630
B' share = 630 * 6
18
= 35 * 6
= ₹ 210
C' share = 630 * 7
18
= 35 * 7
= ₹ 245
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