Please answer these four questions..!
1. If a : b = 7 : 12 and b : c = 3/14 find a/c.
2. If a : b = 3 : 5 and b : c = 6 : 7, find a : b : c.
3. Divide $105 into three parts such that the first part is 4/5 of the second and the ratios between the second and third part is 5 : 6.
4. Two numbers are in the ratio 1 : 4. Their difference is 30. Find the numbers.
Answers
Answer:
1. a/b = 7/12 ……………. (1)
b/c = 3/14 ……………. (2)
Multiplying (1) and (2) we get;
a/b × b/c
= 7/12 × 3/14
= 1/8
Therefore, a/c = 1/8
or, a : c = 1 : 8
2. We have,
a : b = 3 : 5
i.e., a : b = 3/5 : 1
Also, b : c = 6 : 7
i.e., b : c = 1 : 7/6
Therefore, a : b : c
= 3/5 ∶ 1 ∶ 7/6
Taking the L.C.M. of 5 and 6, we get 3
Therefore, a : b : c
= 3/5 × 30 ∶ 1 × 30 ∶ 7/6 × 30
= 18 : 30 : 35
3. Let the ratio of the three parts be a : b : c
a = ⁴/₅b
Therefore, a/b = 4/5
i.e., a : b = 4/5 : 1
Again, b/c = 5/6
Therefore, b/c = 1/(6/5)
i.e., b : c = 1 : 6/5
Therefore, a : b : c = 4/5 : 1 : 6/5
The L.C.M of the denomination is 5
Therefore, a : b : c
= 4/5 × 5 : 1 × 5 : 6/5 × 5
= 4 : 5 : 6
Now, total number of parts = 4 + 5 + 6 = 15
Therefore, first part = 4/15 × 105 = 28
Therefore, second part = 5/15 × 105 = 35
Therefore, third part = 6/15 × 105 = 42
4. Let the common ratio be x. So, the smaller number is 1x.
And the greater number is 4x.
Their difference is 30.
i.e., 4x - x = 30
3x = 30
x = 30/3
x = 10
Therefore, 1x = 1 × 10 = 10
4x = 4 × 10 = 40
Therefore, the two numbers are 10 and 40.
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