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Phrases Previous Year Questions (PYQs)
Phrases Quantitative Aptitude PYQ
A set of consecutive positive integers beginning with
1 is written on the blackboard. A student came along
and erased one number. The average of the remaining
numbers is 35715. What was the number erased?
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Solution
In a city, 40.1% of the adults are illiterate while
85.1% of the children are literate. If the ratio of the
adults to that of the children is 2:3, then what percent
of the population is literate?
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Solution
A runs 123 times as fast as B. If A gives B a start of
80m, how far must the winning post be so that A and
B might reach it at the same time?
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Solution
Mr. Kumar drives to work at an average speed of 48
Km/hr. The time taken to cover the first 60% of the
distance is 10 minutes more than the time taken to
cover the remaining distance. How far is his office?
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Solution
Two pipes A and B can fill the cistern in 37.5
minutes and 45 minutes respectively. Both pipes are
opened. The cistern will be filled in just half an hour,
if the B is turned off after
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Solution
In a shower, 5 cm of rainfalls. The volume of water
that falls on 1.5 hectares of ground is:
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Solution
In a competitive examination in Maharashtra state
9% candidates got selected from the total appeared
candidates. Tripura state had an equal number of
candidates appeared and 12% candidates got selected
with 102 more candidates got selected than
Maharashtra state. What was the number of
candidates appeared from each state?
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Solution
Shiva gave 40% of his monthly salary to his mother
from the remaining he used 7% for electronic gadgets
and 23% he kept aside for his monthly expenses. The
remaining amount he transferred to his friend’s
account. The sum of the amount he gave to his
mother and he transferred to his friend account was
41000. What was Shiva’s monthly salary?
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Solution
In the half yearly exam only 60% of the students were passed. Out of these (passed in half-yearly) only 70% students are passed in annual exam, out of remaining students (who fail in half-yearly exam) 80% passed in annual exam. What percent of the students passed the annual exam?
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Solution
Percentage Word Problem
Given:
- 60% students passed the half-yearly exam.
- Of them, 70% passed the annual exam.
- From the remaining 40% (who failed half-yearly), 80% passed the annual exam.
Assume total students = 100
✅ From 60 students who passed half-yearly:
→ 70% of 60 = 42 passed annual exam.
✅ From 40 students who failed half-yearly:
→ 80% of 40 = 32 passed annual exam.
✅ Total students who passed annual exam = 42 + 32 = 74
Final Answer: 74%
In an examination, 78% of the total students who
appeared were successful. If the total number of
failures was 176 and 34% got first class, then how
many students got first class?
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Solution
If the numerator of a fraction is increased by 25%
and denominator decreased by 20%, the new value is
5/4. What is the original value?
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Solution
Ritu purchased 20 dozen of bananas at the rate of Rs. 375 per dozen. she sold each one of them at the rate of Rs. 33. What was her profit percentage?
Go to Discussion
Solution
Ritu's Profit Percentage on Bananas
Step 1: Ritu purchased 20 dozen bananas.
Cost per dozen = ₹375
Total cost price (CP) = 20 × 375 = ₹7500
Total number of bananas = 20 × 12 = 240
Selling price (SP) per banana = ₹33
Total SP = 240 × 33 = ₹7920
Step 2: Calculate Profit
Profit = SP − CP = 7920 − 7500 = ₹420
Profit % = (Profit / CP) × 100 = (420 / 7500) × 100 = 5.6%
✅ Final Answer: 5.6%
Hemant deposits 10% of his salary in PF. He saves 30% of the remaining salary. The ratio of his expense on medicine and groceries is 3:4 of the remaining salary after saving. If his expense on the medicine was Rs. 2700, then find his monthly salary.
Go to Discussion
Solution
Hemant's Monthly Salary Calculation
Step 1: Let Hemant's monthly salary be x.
He deposits 10% in PF ⇒ PF = 0.10x
Remaining salary after PF = 0.90x
Step 2: Savings
He saves 30% of the remaining ⇒ Savings = 0.30 × 0.90x = 0.27x
Remaining after savings = 0.90x - 0.27x = 0.63x
Step 3: Expenses on Medicine and Groceries
The ratio is given: Medicine : Groceries = 3 : 4
Total ratio parts = 3 + 4 = 7
Medicine = (3/7) × 0.63x = 0.27x
Step 4: Given that medicine expense = Rs. 2700
0.27x = 2700
⇒ x = 2700 ÷ 0.27 = ₹10,000
✅ Final Answer: ₹10,000
Hari invested an amount at a certain rate of interest on simple interest and he got 60% more amount after eight years. If he invests Rs. 9600 at the same rate of interest on simple interest, then find the total interest he would get after four years?
Go to Discussion
Solution
Given: 60% interest in 8 years using Simple Interest (SI).
So, rate (R) = (60 / 8) = 7.5% per annum
Now, SI on ₹9600 for 4 years at 7.5%:
SI = (9600 × 7.5 × 4) / 100 = ₹2880
✅ Final Answer: ₹2880
Two cars, Car A and Car B, are
travelling on a highway. Car A starts from point X and travels at a constant
speed of 60 km/h, while Car B starts from the same point X but travels at a
constant speed of 80 km/hr. If both cars travel for 1.5 hours, what is the
difference in distance covered by Car B compared to Car A?
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Solution
After allowing 20% cash discount, a
trader still earns a profit of 11.11%. How much above the cost price, the
trader marks his goods?
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Solution
A Group of 630 children are seated in n rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
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Solution
405 sweets were distributed equally among a group of children such that the number of sweets received by each child is one-fifth of the number of children. The number of children in the group is
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Solution
A bus starts from its depot filled to seating capacity. It stops at a point A where 1/6th of the passengers alight and 10 board the bus. At point B, 1/5th of the passengers alight and 3 board the bus. At point C which is the last stop, all the 55 passengers alight. The capacity of the bus is
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Solution
If all the 6's are replaced by 9's, then the algebraic sum of all the numbers from 1 to 100 (both inclusive)
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Solution
The greatest number which on dividing
1657 and 2037 leaves remainders 6 and 5
respectively is
Go to Discussion
Solution
The first number = (1657 - 6) = 1651
Second number = (2037 - 5) = 2032
Taking the HCF of two numbers 1651, 2032 we get 127.
So, if we divide 1657 and 2037 by 127 we will get remainders 6 and 5 respectively.
Three cities A, B, C are equidistant from each other.
A motorist travels from A to B at 30km/hour, from B
to C at 40km/hour, and from C to A at 50km/hour.
Then the average speed is
Go to Discussion
Solution
Let distance is x ,so
time t1=x/30,
t2=x/40 and
t3=x/50.
From question same distance so total distance = 3x
total time = x/30+x/40+x/50
so
Average speed = total distance/ total time =3x/(x/30+x/40+x/50)= 1800/47=38.3km/h.
Solution Contribution by Priyanka Soni
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