Question: 11. Simplify the ratio 15:25.
12. In a recipe, the ratio of flour to sugar is 4:1. If 16 cups of flour are used, how many cups of sugar are needed?
13. A man divides 180 between his two sons in the ratio 2:7. How much does the older son receive?
14. 80 is shared among three people in the ratio 1:2:3. How much does the person with the largest share get?
15. If 5 mangoes cost 12.50, how much will 8 mangoes cost?
1. Problem 11: Simplify the ratio $15:25$.
The ratio $15:25$ means $\frac{15}{25}$.
To simplify, find the greatest common divisor (GCD) of $15$ and $25$, which is $5$.
Divide numerator and denominator by $5$:
$$\frac{\cancel{15}^3}{\cancel{25}^5} = \frac{3}{5}$$
So, the simplified ratio is $3:5$.
2. Problem 12: Flour to sugar ratio is $4:1$. If flour is $16$ cups, find sugar cups.
Let sugar cups be $x$.
Set up proportion:
$$\frac{4}{1} = \frac{16}{x}$$
Cross multiply:
$$4x = 16 \times 1 = 16$$
Divide both sides by $4$:
$$x = \frac{16}{4} = 4$$
So, sugar needed is $4$ cups.
3. Problem 13: Divide $180$ in ratio $2:7$ between two sons. Find older son's share.
Total parts = $2 + 7 = 9$.
Older son's share = $\frac{7}{9} \times 180$.
Calculate:
$$\frac{7}{9} \times 180 = 7 \times \frac{180}{9} = 7 \times 20 = 140$$
Older son receives $140$.
4. Problem 14: Share $80$ among three people in ratio $1:2:3$. Find largest share.
Total parts = $1 + 2 + 3 = 6$.
Largest share corresponds to $3$ parts.
Calculate:
$$\frac{3}{6} \times 80 = \frac{1}{2} \times 80 = 40$$
Largest share is $40$.
5. Problem 15: If $5$ mangoes cost $12.50$, find cost of $8$ mangoes.
Cost per mango:
$$\frac{12.50}{5} = 2.5$$
Cost for $8$ mangoes:
$$8 \times 2.5 = 20$$
So, $8$ mangoes cost $20$.
Final answers:
11. $3:5$
12. $4$
13. $140$
14. $40$
15. $20$