💠RulesðŸ’
2) a : b = c : d ie. a : b : : c : d
3) a : x : : x : b ie x square = ab ie x = √ ab
4) a : b : : b : x ie ax=b square ie x=b square/a
5) a : b : : c : x ie a×x = b×c ie x = b×c / x
6) a : d = a : b × b : c × c : d
◼️ Questions and solutions
Q1 | a : b = 2 : 3 b : c = 5 : 3 a : b : c = ?
Ans- 2 : 3 : : 5 : 3. ( 2×5 3×5 3×3 )
10 : 15 : 9
OR .
a : b = ( 2 : 3 ) × 5 = 10 : 15
b : c = ( 5 : 3 ) × 3 = 15 : 9
Ie a : b : c = 10 : 15 : 9
Q2 |. a : b = 2 : 3 ; b : c = 5 : 3 then a : b = ?
Ans- a : c = a/b × b/c
= 2/3 × 5/3
= 10/9
Ie a : b = 10 : 9
Q3 |. a : b = 2 : 3 ; b : c = 3 : 4 ; c : d = 4 : 5 then, a : d = ?
Ans - a : b = a/b × b/c × c/d
= 2/3 × 3/4 × 4/5
= 2/5
a : d = 2 : 5
Q4 | a : b : c = 6 : 8 : 9 & c : d = 15 : 17 then,
a : b : c : d = ?
Ans - a : b : c = ( 6 : 8 : 9 ) × 5
= 30 : 40 : 45
c : d = 45 : 51
Ie a : b : c : d = 30 : 40 : 45 : 51
Q5 |. a : b = 2 : 3 ; b : c = 5 : 4 ; c : d = 12 : 17 then, a : b : c : d = ?
Ans- a : b = ( 2 : 3 ) × 5 = 10 : 15
b : c = ( 5 : 4 ) × 3 = 15 : 12
a : b : c = 10 : 15 : 12
c : d = 12 : 17
Ie. a : b : c : d = 10 : 15 : 12 : 17
OR
a : b. : c : d
×. 2 : 3 : ➡️3 :➡️ 3
× 5⬅️ : 5 : 4 :➡️ 4
× 12⬅️ : 12⬅️ : 12 : 17
120 : 180 : 144 : 204
Ie. 10 : 15 : 12 : 17
Q6 | a : b = 3 : 4 ; b : c = 8 : 9 ; c : d = 15 : 16 then, a : d = ?
Ans- 2A=3B 3B=8C
A/B = 3/2. B/C=8/3
A:B. B:C. _________
3:2. 8:3. | 3×8=24.
| 2×8=16.
| 2×3=6.
A:B:C=12:8:6
2Q.|. The age of sonal and Nitya are in the ratio of 9:5 respectively after 8 years the ratio of their age will be 13:9 what is the difference (in years) between their age ?
Ans-. Sonal : Nitya
9 : 5
9x+8 =13. | After 8 years ratio
5x+8 = 9. | 13 : 9
81x+72= 65x+104
16x=32. | 9×2=18
X=2. | 5×2=10
Sonal : Nitya 18 : 10
OR
Sonal : Nitya
9 : 5. After 8 years
4 {. } 4. 4=8yr
13 : 9.
3Q |. The ratio of their age of Tina and Rakesh 9:10 respectively. 10 years ago the ratio of their age was 4:5 respectively what is the present age of rakesh ?
Ans- Tina : rakesh
9:10. ( Difference 5 )
4:5. ( 10 age )
5 :- 10 years
10 :- 20 years
present age of rakesh 20 years
4Q |. The age of father is 3 time of the age of his son at present 4 years hence the ratio between the ages of father and son becomes 13:5 respectively what is the present age of father ?
Ans - father : son
( 3 : 1 ) × 8
( 13 : 5 ) × 2
24 : 8 ( difference 2 )
26 : 10
2 :- 4 years
24 :- 48 year
the present age of father 48 years
5Q |. If a : b = 5 : 7 the ( 3a+5b) : ( 5a-2b ) = ?
And - a/b = 5/7 =3×5+5×7 / 5×5-2×7
= 15+35 / 25-14. = 50/11
= 50 : 11
6Q |. If A is greater than B by 40% and B is less than C by 20% than what is the value of A : B : C = ?
Ans - A : B = 140 : 100. ( A=100%+40=140 )
B : C = 80 : 100. ( B=100%-20=80 )
Now, A : B : C = A : B : : B : C
= 140 : 100 : : 80 :100
= 7 : 5 : : 4 : 5. (7×4)(5×4)(5×5)
A : B : C = 28 : 20 : 25
7Q |. 675 is total to A and B and their is 5 : 4 find value of A ?
Ans - A : B
5 : 4 = 9 total- 675
9 - 675
1 - 75
value of A :- 5 = 375
B :- 4 = 300
8Q |. In 3 : 5 which smallest value will be added to become 3 : 4 ?
Ans - 3 : 5 = 3 + x / 5 + x = 3/4
12 + 4x = 15 + 3x
x = 15 - 12
x = 3
9Q |. 6A = 4B = 9C. A : B : C = ?
Ans - 6A = 4B
A / B = 3 / 2
I.e A : B = 2 : 3 B : C = 9 : 4
18 : 27 : 12
6 : 9 : 4
A : B : C = 6 : 9 : 4
10Q |.
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