Practice Questions
Divide ₹840 in the ratio 4:5:6.
Sum of ratios = $4+5+6 = 15$. Parts are $(4/15) \times 840 = 224$, $(5/15) \times 840 = 280$, and $(6/15) \times 840 = 336$.
If a:b = 3:4 and b:c = 5:6, find a:b:c.
Make 'b' common: multiply (3:4) by 5 and (5:6) by 4. Result: 15:20:24.
The ratio of two numbers is 7:11. If 10 is added to each, the ratio becomes 9:13. Find the numbers.
$(7x+10)/(11x+10) = 9/13 \Rightarrow 91x + 130 = 99x + 90 \Rightarrow 8x = 40 \Rightarrow x = 5$. Numbers are 35 and 55.
A sum of money is divided among A, B and C in ratio 2:3:5. If C gets ₹500 more than A, find total sum.
Difference between C and A is $5x - 2x = 3x$. $3x = 500 \Rightarrow x = 500/3$. Total sum = $(2+3+5)x = 10x = 10 \times 500/3 = 1666.67$.
If 12 men can complete a work in 15 days, how many men are required to complete it in 9 days?
Using $M_1 \times D_1 = M_2 \times D_2$: $12 \times 15 = 180$. $M_2 = 180 / 9 = 20$.
Find the fourth proportional to 8, 12 and 18.
$8:12 = 18:x \Rightarrow 8x = 12 \times 18 \Rightarrow x = 216 / 8 = 27$.
In a partnership, A invests ₹5000 for 12 months and B invests ₹8000 for 9 months. Find profit sharing ratio.
Profit Ratio = $(5000 \times 12) : (8000 \times 9) = 60000 : 72000 = 5 : 6$.
The income of A and B are in ratio 3:4 and their expenditures in ratio 2:3. If both save ₹2000, find their incomes.
Let incomes be $3x, 4x$. Savings = Income - Expenditure $\Rightarrow 3x - 2y = 2000, 4x - 3y = 2000$. Solving gives $x = 2000$. Incomes are ₹6000 and ₹8000.
If x varies directly as y and x = 15 when y = 5, find x when y = 12.
$x = ky \Rightarrow 15 = 5k \Rightarrow k = 3$. So when $y=12, x = 3 \times 12 = 36$.
If a:b = 2:3 and b:c = 4:5, find a:c.
a:b = 2:3 = 8:12, b:c = 4:5 = 12:15. So a:c = 8:15.
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