Advertisements
Advertisements
Question
If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` prove that each ratio’s equal to : `(x + y + z)/(a + b + c)`
Solution
`x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` = k(say)
x = k(b + c – a),
y = k(c + a – b),
z = k(a + b – c)
`(x + y + z)/(a + b + c)`
= `(k(b + c - a) + k(c + a - b) + k(a + b - c))/(a + b + c)`
= `(k(b+ c- a + c + a - b + a + b - c))/(a +b + c)`
= `(k(a + b + c))/(a + b + c)`
= k.
Hence proved.
APPEARS IN
RELATED QUESTIONS
By increasing the cost of entry ticket to a fair in the ratio 10 : 13, the number of visitors to the fair has decreased in the ratio 6 : 5. In what ratio has the total collection increased or decreased?
Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-duplicate ratio of 36 : 49.
Find the mean proportional between 0.6 and 9.6
If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z.
In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C, Rs 80000 for 5 months. If they together earn Rs 18800 find the share of each.
Fill in the place holder:
A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?
Find the value of x when 36 : x : : x : 16.
Find the simplified form of the following ratio.
12 : 27
In a year, Seema earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of money that Seema earns to the money she saves.
