Proportional Reasoning-2: questions with answers

1 cm on the map stands for 60,00,000 cm on the ground, which is 60 km. So 5 cm stands for $5 \times 60 = 300$ km.

Proportional ratios have equal cross products, so $6 \times d = 3 \times 4 = 12$. That gives $d = 12 \div 6 = 2$.

White is 5 parts and 5 parts is 10 litres, so 1 part is 2 litres. Red is 2 parts, so red is $2 \times 2 = 4$ litres.

The HCF of 12, 10, 8, 6 and 4 is 2. Dividing every term by 2 gives 6 : 5 : 4 : 3 : 2, and $6 + 5 + 4 + 3 + 2 = 20$.

Congruent triangles have exactly the same sidelengths. Sides 3, 4, 5 and 9, 12, 15 keep the ratio 3 : 4 : 5 but are a different size.

The three angles add to 180°. Divide 180 by the sum of the terms: $180 \div (1 + 3 + 5) = 20$. The angle at A is $1 \times 20 = 20°$.

Add the terms: $4 + 3 + 3 = 10$. The whole is divided by this sum, $150 \div 10 = 15$, and each term is multiplied by 15. Red paint is $4 \times 15 = 60$ ml.

The whole circle is 360° and the class has 40 students, so each student gets $360 \div 40 = 9^\circ$. Grade B has 10 students: $10 \times 9 = 90^\circ$.

Each angle is measured from the radius drawn just before it, so the angles add up as you go round. From AB to AE is 108 + 90 + 72 = 270°.

The Car slice is 360 − 330 = 30°, which is $\frac{1}{12}$ of the circle. So 18 children are $\frac{1}{12}$ of the total, and the total is $18 \times 12 = 216$.

Their hourly rates add to $1 + 2/3 = 5/3$ of the work. Together they take $1 \div (5/3) = 3/5$ hours.

Twice the length of cloth costs twice as much at a fixed rate, so length and price change by the same factor in the same direction. More taps, a faster cyclist or more painters all mean less time, so those pairs are inverse.

One tank takes 6 divided by 2, or 3 hours. Five tanks take 5 times 3, or 15 hours.

Half as many workers need twice as many days. The time is $20 \times 4 \div 10 = 8$ days.

A day is 24 hours and the whole ring is 360°. The sleeping band is 270°, so the hours are $24 \times \frac{270}{360} = 18$.