Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If p, q, r, s are proportional, then (p – q) (p – r)/p =
Explanation
Assume a set of values for p, q, r, s such that they are proportional i.e. p/q = r/s.
Suppose we take p:q, as 1:4 and r:s as 3:12 we get the given expression: (p – q)(p – r)/p = – 3 × – 2/1 = 6.
This value is also given by p + s – q – r and hence option (b) is correct.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If x varies inversely as y^{3} – 1 and is equal to 3 when y = 2, find x when y = 4.
Explanation
x = k/(y^{3} – 1). This gives k = 3 × 7 = 21.
When, y = 4, the equation becomes x = 21/(4^{3} – 1) = 21/63 = 1/3.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:X varies jointly as Y and Z; and X = 6 when Y = 3, Z = 2; find X when Y = 5, Z = 7.
Explanation
X = K × Y × Z → It is known that when X = 6, Y = 3 and Z = 2.
Thus we get 6 = 6K → K = 1.
Thus, our relationship between X, Y and Z becomes X = Y × Z.
Thus, when Y = 5 and Z = 7 we get X = 35.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:Divide ₹ 1400 into three parts in such a way that half of the first part, one-fourth of the second part and one-eighth of the third part are equal.
Explanation
Solve this question using options. 1/2 of the first part should equal 1/4th of the second part and 1/8th of the third part. Only, option (b) satisfies these conditions thus this option is correct
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If 3x^{2} + 3y^{2} = 10xy, what is the ratio of x to y?
Explanation
Solve using options. It is clear that a ratio of x:y as 1: 3 fits the equation
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If 3 examiners can examine a certain number of answer books in 10 days by working 4 hours a day, for how many hours a day would 4 examiners have to work in order to examine thrice the number of answer books in 30 days?
Explanation
3 × 10 × 4 = 120 man-hours are required for ‘x’ no. of answer sheets.
So, for ‘3x’ answer sheets we would require 360 man-hours = 4 × 30 × n → n = 3 Hours a day.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If three numbers are in the ratio of 1 : 3 : 5 and half the sum is 9, then the ratio of cubes of the numbers is:
Explanation
1 : 3 : 5 → x, 3x and 5x add up to 18.
So the numbers are: 2, 6 and 10. Ratio of cubes = 8 : 216 : 1000 = 1: 27: 125.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:The ratio between two numbers is 7 : 11 and their LCM is 154. The first number is:
Explanation
The numbers would be 7x and 11x and their LCM would be 77x. This gives us the values as 14 and 22. The first number is 14.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:P and Q are two alloys of aluminum and brass prepared by mixing metals in proportions 7: 2 and 7: 11, respectively. If equal quantities of the two alloys are melted to form a third alloy R, the proportion of aluminum and brass in R will be:
Explanation
Since equal quantities are being mixed, assume that both alloys have 18 kgs (18 being a number which is the LCM of 9 and 18).
The third alloy will get, 14 kg of aluminum from the first alloy and 7 kg of aluminum from the second alloy.
Hence, the required ratio: 21:15 = 7:5
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If 10 men working 6 hours a day can do a piece of work in 15 days, in how many days will 20 men working 14 hours a day do the same work?
Explanation
The total number of man-days-hours required = 10 × 6 × 15 = 900
20 × 14 × number of days = 900 → number of days = 900/280 = 3.21 days
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:If the ratio of sines of angles of a triangle is 1 : 1 : √2 then the ratio of square of the greatest side to sum of the squares of other two sides is
Explanation
The given ratio for sines would only be true for a 45 - 45 - 90 triangle.
The sides of such a triangle are in the ratio 1:1: √2.
The square of the longest side is 2 while the sum of the squares of the other two sides is also 2.
Hence, the required ratio is 1:1.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:Divide ₹1360 among p, q and r such that p gets 2/3 of what q gets and q gets 1/4th of what r gets. Now the share of r is:
Explanation
p gets 2/3 of what q gets and q gets 1/4th of what r gets’ means a ratio of 2 : 3 : 12 for p : q : r.
Hence, r’s share = 12/17 × 1360 = 960.
Alternately, you could also solve by using options. Option (a) r = 960 fits perfectly because if r = 960, q = 240 and p = 160.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:The students in three batches at Mindworkzz are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio changes to 4 : 5 : 7. The total number of students in the three batches before the increases were
Explanation
2x + 20 : 3x + 20 : 5x + 20 = 4 : 5 : 7 → x = 10 and initially the number of students would be 20, 30 and 50 → a total of 100.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:The speeds of three bikes are in the ratio 1 : 2 : 3. The ratio between the times taken by these bikes to travel the same distance is
Explanation
The ratio of time would be such that speed × time would be constant for all three. Thus if you take the speeds as x, 2x and 3x respectively, the times would be 6y, 3y and 2y, respectively.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:The difference between two positive numbers is 11 and the ratio between them is 2: 1. Find the product of the two numbers.
Explanation
Their ratio being 2: 1, the difference according to the ratio is 11 so the numbers must be 22 and 11 respectively.
Hence, the product is 242.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:A cow takes 5 leaps for every 4 leaps of a goat, but 3 leaps of the goat are equal to 4 leaps of the cow. What is the ratio of the speed of the cow to that of the goat?
Explanation
Assume that 1 cow leap is equal to 3 metres and 1 goat leap is equal to 4 metres. Then the speed of the cow in one unit time = 3 × 5 = 15 meters.
Also, the speed of the goat in one unit time = 4 × 4 = 16 meters.
The required ratio is 15:16.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:The present ratio of ages of P and Q is 3: 5. 10 years ago, this ratio was 1: 2. Find the sum total of their present ages.
Explanation
3x, and 5x are their current ages. According to the problem, 3x – 10 : 5x – 10 = 1:2 → x = 10 and hence the sum total of their present ages is 80 years (30 + 50 = 80).
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:Four numbers in the ratio 1:2 : 4 : 8 add up to give a sum of 120. Find the value of the biggest number.
Explanation
x + 2x + 4x + 8x = 120 → x = 8 Thus, 8x = 64.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:25 students can do a job in 12 days, but on the starting day, five of them informed that they are not coming. By what fraction will the number of days required for doing the whole work get increased?
Explanation
25 × 12 = 300 man-days is required for the job.
If only 20 students turn up, they would require 15 days to complete the task.
The number of days is increasing by 1/4.
Question for Practice Questions Level 1: Ratio & Proportion - 2
Try yourself:A dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol and thus made up 36 litres of petrol. If he now adds 15 litres of petrol to the mixture, find the ratio of petrol and water in the new mixture.
Explanation
The initial amount of water is 9 litres and petrol is 27 litres.
By adding 15 litres of petrol the mixture becomes 42 petrol and 9 water → 14:3 the required ratio.