CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 48

Answer: (c) \( 100 \) machines

Explanation:
1. Money \( =75\times200=15000 \).
2. New price \( =150 \); machines \( =100 \).

Teacher's Note:
1. Same money, lower price.

Answer: (a) \( 196:289 \)

Explanation:
1. Duplicate ratio means squares: \( 14^2:17^2=196:289 \).

Teacher's Note:
1. Duplicate ratio is the ratio of squares.

Answer: (b) (i) and (ii) only

Explanation:
1. (i) \( 440\div4=110 \): numbers \( 330,110 \) true.
2. (ii) true.
3. (iii) numbers \( 12 \) and \( 15 \), product \( 180 \): false.
4. (iv) \( 3k=27 \), \( k=9 \); numbers \( 72 \) and \( 45 \), sum \( 117 \): false.

Teacher's Note:
1. Solve each statement fully.

Answer: (c) \( 58:77 \)

Explanation:
1. Water: \( \frac25\times1+\frac49\times2=\frac{58}{45} \). Milk: \( \frac35\times1+\frac59\times2=\frac{77}{45} \).
2. Ratio \( =58:77 \).

Teacher's Note:
1. Convert each vessel to fractions of water and milk.

Answer: (c) \( 4:5 \)

Explanation:
1. Subduplicate ratio means the square roots: \( \sqrt{16}:\sqrt{25}=4:5 \).

Teacher's Note:
1. Sub-duplicate is the square root ratio.

Answer: (c) \( 234 \) days

Explanation:
1. Remaining food lasts \( 195 \) days for \( 120 \) men.
2. \( 100 \) men: \( 120\times195=100\times x \), so \( x=234 \) days.

Teacher's Note:
1. Fewer men means the food lasts longer.

Answer: (d) Rs. \( 78.75 \)

Explanation:
1. Total weight \( =32\times0.9=28.8 \) kg, so price per kg \( =\frac{84}{28.8}=\frac{35}{12} \).
2. \( 27 \) kg costs \( 27\times\frac{35}{12}=78.75 \).

Teacher's Note:
1. Reduce to price per kg.

Answer: (a) \( 1:3 \)

Explanation:
1. Cost price of the mixture \( =\frac{21.60}{1.2}= \) Rs. \( 18 \) per kg.
2. Quantity of Rs. \( 15 \) sugar : quantity of Rs. \( 19 \) sugar \( =(19-18):(18-15)=1:3 \).

Teacher's Note:
1. Each quantity is proportional to the distance of the other price from the mean price.

Answer: (b) \( 20 \)

Explanation:
1. Money \( =25\times500=12500 \).
2. New price \( =625 \); cycles \( =\frac{12500}{625}=20 \).

Teacher's Note:
1. Total money stays the same.

Answer: (b) \( 1:1 \)

Explanation:
1. \( \frac{5\times15\times98}{7\times14\times75}=\frac{7350}{7350}=1 \).
2. The ratio is \( 1:1 \).

Teacher's Note:
1. Cancel common factors before multiplying.

Answer: (a) Rs. \( 90.10 \), Rs. \( 108.12 \), Rs. \( 126.14 \)

Explanation:
1. Total parts \( =18 \); one part \( =\frac{324.36}{18}=18.02 \).
2. Shares: \( 5\times18.02=90.10 \), \( 6\times18.02=108.12 \), \( 7\times18.02=126.14 \).

Teacher's Note:
1. Find the value of one part first.

Answer: (a) Rs. \( 12750 \)

Explanation:
1. One worker-day \( =\frac{7500}{60}=125 \).
2. \( 17\times6\times125=12750 \).

Teacher's Note:
1. Wages are proportional to worker-days.

Answer: (d) \( 2:1 \)

Explanation:
1. \( x^2-4xy+4y^2=0 \), i.e. \( (x-2y)^2=0 \).
2. So \( x=2y \) and \( x:y=2:1 \).

Teacher's Note:
1. Recognise a perfect square.

Answer: (a) \( 12 \)

Explanation:
1. \( 6:8=9:x \), so \( x=\frac{8\times9}{6}=12 \).

Teacher's Note:
1. For \( a:b=c:x \), \( x=\frac{bc}{a} \).

Answer: (d) \( 1:2 \)

Explanation:
1. Milk fractions: \( \frac34 \) and \( \frac58 \); target \( \frac23 \).
2. First : second \( =\left(\frac23-\frac58\right):\left(\frac34-\frac23\right)=\frac1{24}:\frac1{12}=1:2 \).

Teacher's Note:
1. Use alligation on the fraction of milk.

Answer: (b) Rs. \( 22.5 \)

Explanation:
1. \( 8:9=20:x \), so \( x=\frac{9\times20}{8}=22.5 \).

Teacher's Note:
1. Scale by \( \frac{20}{8}=2.5 \).

Answer: (d) \( 167:148 \)

Explanation:
1. Water: \( \frac37+\frac{20}{9}=\frac{167}{63} \). Milk: \( \frac47+\frac{16}9=\frac{148}{63} \).
2. Ratio \( =167:148 \).

Teacher's Note:
1. Use fractions of water in each vessel.