Ratio - Study Mode

[#166] Two numbers are in ratio P : Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to $$frac{{ ext{R}}}{{ ext{S}}}$$. again, when 1 is added to both the numerator and denominator, it becomes $$frac{1}{2}$$. Find the sum of P and Q.
Correct Answer

(C) 5

Explanation

Solution: If we go through normal method, It will be quite cumbersome,so, We will solve this question through options Taking Option A: It has P + Q = 3. The possible value of $$frac{{ ext{P}}}{{ ext{Q}}}$$ is $$frac{1}{2}$$ or $$frac{2}{1}$$
Using $$frac{1}{2}$$, we see that on adding 2 in both the numerator and denominator we get $$frac{3}{4}$$ (not required value)
Similarly we check for $$frac{2}{1}$$, this will also not give the required value Option B: We have $$frac{1}{3}$$ possible ratio Then, we get the final value as $$frac{3}{5}$$ (not = to $$frac{1}{2}$$) Hence, rejected Option C: Here we have $$frac{1}{4}$$ or $$frac{2}{3}$$ Checking for $$frac{1}{4}$$ we get $$frac{3}{6}$$ = $$frac{1}{2}$$ Hence, the option c is correct

[#167] The ratio of water and milk in a 30 liter mixture is 7 : 3. Find the quantity of water to be added to the mixture in order to make this ratio 6 : 1.
Correct Answer

(C) 33

Explanation

Solution: Here,Let water = 7x and milk = 3x
Now, 7x + 3x = 30 x = 3 So, water = 7x = 7 × 3 = 21 liter Milk = 3x = 3 × 3 = 9 liter Now, we keep milk constant and add water to mixture to get ratio 6 : 1 Let water in this mixture = 6y and milk = y We have, milk = 9 liter, so y = 9 liter Water = 6y = 6 × 9 = 54 liter Then extra water to be added is 33 liter

[#168] The incomes of A and B are in the ratio 3 : 2 and their expenditure are in ratio 5 : 3. If each saves Rs. 1000, then, A's income can be:
Correct Answer

(C) Rs. 6000

Explanation

Solution: Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y. Now, according to question, 3x - 5y = 1000 ------- (i) × 3 2x - 3y = 1000 ---------- (ii) × 5 9x - 15y - 10x + 15y = 3000 - 5000 Or, -x = -2000 Or, x = 2000 Then, income of A = 3x = 3 × 2000 = Rs. 6000

[#169] The difference between two positive numbers is 10 and the ratio between them is 5 : 3. Find the product of the two numbers.
Correct Answer

(A) 375

Explanation

Solution: Let the two positive numbers be 5x and 3x respectively According to question, 5x - 3x = 10 Or, x = 5 Then numbers are 25 and 15 Thus, their product = 25 × 15 = 375

[#170] If 30 oxen can plough $$frac{1}{7}$$ th of a field in 2 days, how many days 18 oxen will take to do the remaining work?
Correct Answer

(B) 20 days

Explanation

Solution: We will use work equivalence method, $$eqalign{
& frac{{30}}{{18}} = frac{{ {frac{1}{7}} }}{{ {frac{6}{7}} }} imes frac{x}{2} cr
& frac{5}{3} = {frac{1}{6}} imes frac{x}{2} cr
& Or,,x = frac{{60}}{3} = 20,{ ext{days}} cr} $$