1. Find the third proportion to the number 9 and 6.
Sol:
a = 9
b = 6
2. Two numbers are in the ratio 3:7. If sum of these two numbers is 180, find the difference between the numbers.
Sol:
(3 + 7) ⟶ 180
1 unit ⟶ 18
difference = 7 – 3 = 4 unit = 4 × 18 = 72 Answer
3. If sum of three numbers is 171 and the ratio between the first and second be 3:5 and that between second and third be 4:5 then find the second number.
Sol:
Let numbers be a, b, c
\(\frac{a}{b} = \frac{3}{5}\) ⟶ \(\frac{{3 \times 4}}{{5 \times 4}}\) ⟶ \(\frac{{12}}{{20}}\)
\(\frac{b}{c} = \frac{4}{5}\) ⟶ \(\frac{{4 \times 5}}{{5 \times 5}}\) ⟶ \(\frac{{20}}{{25}}\)
∴ (12 + 20 + 25) ⟶ 171
1 unit ⟶ 3
∴ second number = 20 unit = 20 × 3 = 60 Answer
4. A bag contains an equal number of 50-paise, 25-paise, 20-paise coins. If the total amount is Rs. 60, how many coins of each type are there ?
Sol:
x × (50 + 25 + 20 + 5) = 60 × 100
x = 60
So bag has 60 coins of each type Answer
5. The ratio of two numbers is 11:7. If each number be decreased by 3, the two numbers are in the ratio 5:3. Find the numbers.
Sol:
Ratio of numbers = 11:7
Let first number = 11x
& second number = 7x
∴ \(\frac{{11x – 3}}{{7x – 3}} = \frac{5}{3}\) ⟹ x = 3
∴ numbers are:
11 × 3 = 33
& 7 × 3 = 21 Answer
6. The ratio of income of two persons is 7:4 and that of their expenditure is 3:5. Find the income of each person, if they save Rs. 460 and Rs. 230 respectively.
Sol:
Income 7 : 4
expenditure 3 : 5
saving 460 Rs. 230 Rs.
∴ \(\frac{{7x – 460}}{{4x – 230}} = \frac{3}{5}\)
35x – 2300 = 12x – 690
23x = 1610
x = 70
∴ Income are:
7 × 70 = 490 Rs.
4 × 70 = 280 Rs. Answer
7. Divide Rs. 2160 into three parts in such a way that half of the first part, one-third of the second part and one-seventh of the third part are equal.
Sol:
\(\frac{x}{2} = \frac{y}{3} = \frac{z}{7}\)
∴ x : y : z = 2 : 3 : 7 ⟶ (2 + 3 + 7) ⟶ 2160
1 unit ⟶ 180
∴ x = 2 × 180 = 360 Rs.
y = 3 × 180 = 540 Rs.
z = 7 × 180 = 1260 Rs. Answer
8. After an increament of 5 in both the numerator and denominator, a fraction changes to \(\frac{4}{5}\). Find the original fraction.
Sol:
Let original fraction = \(\frac{x}{y}\)
∴ \(\frac{{x + 5}}{{y + 5}} = \frac{4}{5}\) ⟹ 5x = 4y – 5
So ratio of x & y can’t be determined. Answer
9. The student in classes of a school are in the ratio 3:5:7. If 30 student are increased in each class, the ratio changes to 3:4:5. Find total number of students in each class before increase.
Sol:
10. If \(\frac{1}{x}:\frac{1}{y}:\frac{1}{z}\) = 3:4:5 then find x : y : z.
Sol:
x : y : z = \(\frac{1}{3}:\frac{1}{4}:\frac{1}{5}\)
x : y : z = \(\frac{{60}}{3}:\frac{{60}}{4}:\frac{{60}}{5}\)
= 20 : 15 : 12 Answer