Algebra word Problems(LEVEL - 2 )
Q1–10 of 50The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?
Remaining fluid fraction
Calculation: Let bucket volume $= V$. Large bottle capacity $L = \frac{V}{4}$, Small bottle capacity $S = \frac{V}{7}$.
Fraction transferred from $L$ to fill $S = \frac{S}{L} = \frac{V/7}{V/4} = \frac{4}{7}$.
Fraction left in $L = 1 - \frac{4}{7} = \frac{3}{7}$.
Correct Answer: (b) 3/7
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
Calculation: Let initial bucket capacity $= C$. Tank capacity $= 25C$.
New bucket capacity $= \frac{2}{5}C$.
Buckets needed $= \frac{25C}{\frac{2}{5}C} = \frac{125}{2}$.
Correct Answer: (c) 125/2
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number of questions he answered correctly was
Correctly answered questions
Calculation: Let $x$ be correct answers. Incorrect $= 200 - x$.
$4x - 1(200 - x) = 200 \implies 5x - 200 = 200 \implies 5x = 400 \implies x = 80$.
Correct Answer: (c) 80
On a 26 question test, five points were deducted for each wrong answer and eight points were credited for each correct answer. If all the questions were answered, how many were correct if the score was zero?
Correct answers for zero score
Calculation: Let correct $= c$, wrong $= w$.
$c + w = 26$ and $8c - 5w = 0 \implies w = \frac{8}{5}c$.
$c + \frac{8}{5}c = 26 \implies \frac{13}{5}c = 26 \implies c = 10$.
Correct Answer: (c) 10
In an examination, a student attempted 15 questions correctly and secured 40 marks. If there were two types of questions (2 marks and 4 marks questions), how many questions of 2 marks did he attempt correctly?
2-mark questions answered correctly
Calculation: Let $x$ be 2-mark questions, $y$ be 4-mark questions.
$x + y = 15 \implies y = 15 - x$.
$2x + 4(15 - x) = 40 \implies 60 - 2x = 40 \implies 2x = 20 \implies x = 10$.
Correct Answer: (b) 10
In an examination there are 30 questions. 1 mark is given for each correct answer and 0.25 is deducted for each incorrect answer. Ankur attempted all the questions and scored 13.75. How many incorrect answers did he have?
Number of incorrect answers
Calculation: Let correct $= c$, incorrect $= w$.
$c + w = 30 \implies c = 30 - w$.
$1(30 - w) - 0.25w = 13.75 \implies 30 - 1.25w = 13.75 \implies 1.25w = 16.25 \implies w = 13$.
Correct Answer: (d) None of these (13)
For aiming at a target a person gets one rupee each time when he hits it and loses one rupee when he misses it. If he gets ₹30 after aiming at the target one hundred times, then how many times did he miss the target?
Times target missed
Calculation: Let hits $= h$, misses $= m$.
$h + m = 100$ and $h - m = 30$.
Subtracting gives $2m = 70 \implies m = 35$.
Correct Answer: (b) 35
There are some cows, bulls and 45 hens in a group. One caretaker looks after 15 animals. The number of bulls is twice the number of cows. If the number of heads is less than the total number of feet by 186 (including the caretakers), how many caretakers are there?
Number of caretakers
Calculation: Let cows $= C$, bulls $= 2C$, hens $= 45$.
Total animals $= 3C + 45$.
Caretakers $K = \frac{3C + 45}{15} = \frac{C + 15}{5}$.
Total heads $= 3C + 45 + K$.
Total feet $= 4(3C) + 2(45) + 2(K) = 12C + 90 + 2K$.
$(12C + 90 + 2K) - (3C + 45 + K) = 186 \implies 9C + 45 + K = 186 \implies 9C + K = 141$.
Substituting $K = \frac{C + 15}{5}$: $9C + \frac{C + 15}{5} = 141 \implies 46C + 15 = 705 \implies 46C = 690 \implies C = 15$.
$K = \frac{15 + 15}{5} = 6$.
Correct Answer: (b) 6
A man's basic pay for a 40 hours' week is ₹200. Overtime is paid at 25% above the basic rate. In a certain week, he worked overtime and his total was ₹300. He, therefore, worked a total of (in hours)
Total hours worked
Calculation: Basic rate $= \frac{200}{40} = ₹5/\text{hr}$.
Overtime rate $= 5 \times 1.25 = ₹6.25/\text{hr}$.
Overtime pay $= 300 - 200 = ₹100$.
Overtime hours $= \frac{100}{6.25} = 16\text{ hrs}$.
Total hours $= 40 + 16 = 56\text{ hrs}$.
Correct Answer: (b) 56
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets ₹24 per hour for regular work and ₹32 per hour for overtime. If he earns ₹4320 in 4 weeks, then how many hours does he work for?
Calculation: Regular hours in 4 weeks $= 4 \times 5 \times 8 = 160\text{ hrs}$.
Regular pay $= 160 \times 24 = ₹3840$.
Overtime pay $= 4320 - 3840 = ₹480$.
Overtime hours $= \frac{480}{32} = 15\text{ hrs}$.
Total hours $= 160 + 15 = 175\text{ hrs}$.
Correct Answer: (b) 175