Practice UPSC CSAT previous year questions from 2011–2026 classified underRatio and Proportion. Review the original question, four options, correct answer and explanation for every PYQ.
19 questions • 2011–2026
The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
Take 10 female workers in each company. A then has 13+10=23 total workers; B has 14+10=24. Ratio =23:24. Hence B.
Two persons P and Q enter into a business. P puts ₹14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is ₹400 more than Q's share out of the total profit of ₹2,000, what is the capital contributed by P?
Profit shares are ₹1,200 and ₹800, so capital×time is in the ratio 3:2. With times 8 and 10 months, P/Q capital ratio is (3/2)×(10/8)=15/8. Since P exceeds Q by ₹14,000, Q=₹16,000 and P=₹30,000.
A person buys three articles P, Q and R for ₹3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?
Let Q=x. Then R=1.2x and P=1.25R=1.5x. Total 3.7x=3330, so x=900 and P=₹1,350.
A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?
If A receives x pens, the other amounts are x/2, x/3, x/4, x/5 and x/6. x must be a multiple of 60, and to make x/4 even the minimum is x=120. The total is 120+60+40+30+24+20=294.
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?
0.7x+y=1.65y gives y=(0.7/0.65)x=14x/13. Similarly 0.6x+z=1.65z gives z=(0.6/0.65)x=12x/13. Hence z<x<y.
Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct?
Let pen=p and pencil=c. Equal spending gives 3p+5c=2p+7c, hence p=2c.
An amount of money was distributed among A, B and C in the ratio p:q:r. Consider the following statements: 1. A gets the maximum share if p is greater than (q+r). 2. C gets the minimum share if r is less than (p+q). Which of the above statements is/are correct?
If p>q+r, p is certainly larger than each of q and r. But r<p+q does not ensure r is smaller than both p and q; statement 2 is not sufficient.
A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
Multiply the ratio by 12 to get 6:9:10. Total 25 parts equals Rs.2500, so the difference is 4 parts = Rs.400.
A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Let empty weight be E and full water weight be W. E+W=40 and E+W/3=20, so 2W/3=20, W=30 and E=10 kg.
In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?
18 is three-fourths of the boys, so there are 24 boys. If boys are two-thirds of the class, total students are 36; therefore girls = 36−24=12.
The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay.
The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is:
Total emoluments are 1.65 times the first basic pay and 1.80 times the second. Thus basic-pay ratio = 1.80:1.65 = 12:11.
An automobile owner reduced his monthly petrol consumption when the prices went up. The price-consumption relationship is as follows: Price (in ₹ per litre): 40, 50, 60, 75 Monthly consumption (in litres): 60, 48, 40, 32 If the price goes up to ₹80 per litre, his expected consumption (in litres) will be
The observed relation is inverse: price × consumption = 40×60 = 50×48 = 60×40 = 2400. Thus at ₹80, consumption = 2400/80 = 30 litres.
Each of A, B, C and D has ₹100. A pays ₹20 to B, who pays ₹10 to C, who gets ₹30 from D. In this context, which one of the following statements is not correct?
Final amounts are A=80, B=110, C=140 and D=70. C does not exceed A+D, because 140 < 80+70=150.
In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is
If cars=x and two-wheelers=y, 4x+2y=2(x+y)+100, giving 2x=100 and x=50.
A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of black and brown pairs by mistake which increased the bill by 100%. What was the number of pairs of brown socks in the original order?
Let a brown pair cost x and let n be the number of brown pairs. Original bill = (15+n)x; swapped bill = (5+3n)x. Doubling gives 5+3n=30+2n, so n=25.
The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves ₹6,000 at the end of the month, their monthly incomes respectively are (in ₹)
Let incomes be 4x and 3x and expenses 3y and 2y. Equal savings give 4x−3y=6000 and 3x−2y=6000, yielding x=6000 and incomes ₹24,000 and ₹18,000.
A cow costs more than 4 goats but less than 5 goats. If a goat costs between ₹600 and ₹800, which of the following is a most valid conclusion?
A cow costs more than 4 goats, so it is above ₹2,400; it costs less than 5 goats, so it is below ₹4,000. Thus D gives the valid overall range.
There are some balls of red, green and yellow colour lying on a table. There are as many red balls as there are yellow balls. There are twice as many yellow balls as there are green ones. The number of red balls
If yellow = red and yellow = 2×green, then red = 2×green.
Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?
Milk = 1/2 + 3/4 = 5/4 of a glass. Water = 1/2 + 1/4 = 3/4. Ratio = 5:3.
Attempt questions one by one with UPSC-style marking and immediate explanations.