Sure, let's break down each part of the question step-by-step:
### Section 1: Ratios
1.J a)
- Question: Ratio of 3 to 4 is ___ antecedent is ___ consequent is ___
- Answer:
- Ratio: [tex]\( 3:4 \)[/tex]
- Antecedent: 3
- Consequent: 4
1.J b)
- Question: Ratio of 1 kg to 500 g is ___ antecedent is ___ consequent is ___
- Answer:
- Ratio: [tex]\( 1000:500 \)[/tex]
- Antecedent: 1000 (since [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex])
- Consequent: 500
1.J c)
- Question: The compounded ratio of [tex]\( p : q \)[/tex] and [tex]\( r : s \)[/tex] is ___
- Answer: The compounded ratio is [tex]\( \frac{p \cdot r}{q \cdot s} \)[/tex]
1.J d)
- Question: The compounded ratio of [tex]\( 1 : 4 \)[/tex] and [tex]\( 3 : 1 \)[/tex] is ___
- Answer: The compounded ratio is [tex]\( 0.75 \)[/tex]
1.J e)
- Question: If [tex]\( \frac{a}{b} = \frac{1}{2} \)[/tex] and [tex]\( \frac{b}{c} = \frac{2}{3} \)[/tex], then [tex]\( \frac{a}{c} = \)[/tex] ___
- Answer: [tex]\( \frac{a}{c} = 0.3333333333333333 \)[/tex] (which is [tex]\(\frac{1}{3}\)[/tex])
1.J f)
- Question: If [tex]\( x : y = 1 : 2 \)[/tex] and [tex]\( y : z = 4 : 3 \)[/tex], then [tex]\( x : z = \)[/tex] ___
- Answer: [tex]\( x : z = 0.6666666666666666 \)[/tex] (which is [tex]\(\frac{2}{3}\)[/tex])
### Section 2: Application of Ratios
2.a)
- Question: Two numbers are in the ratio [tex]\( 1 : 2 \)[/tex]. If the smaller one is 5, the greater one is:
- Answer: The greater number is [tex]\( 10.0 \)[/tex]
2.b)
- Question: Two sums are in the ratio [tex]\( 3 : 1 \)[/tex] and the first sum is Rs 30, the second sum is:
- Answer: The second sum is Rs [tex]\( 10.0 \)[/tex]
2.c)
- Question: Two weights are in the ratio [tex]\( 1 : 4 \)[/tex] and the second weight is 20 kg, the first is:
- Answer: The first weight is [tex]\( 5.0 \text{ kg} \)[/tex]
These answers should cover each part of the question comprehensively.
