## 19th SSC CGL Tier II level Solution Set, 2nd on topic Profit and loss

This is the 19th solution set of 10 practice problem exercise for SSC CGL Tier II exam and 2nd on topic Profit and loss. Students should complete the corresponding question set in prescribed time first and then only refer to this solution set for extracting maximum benefits from this resource.

We will repeat here the method of taking a 10 problem test if you have not gone through it already. And if you have not taken the test yet, you can refer to * SSC CGL Tier II level Question Set 19, Profit and loss 2*, and then after taking the test come back to this solution.

### Method for taking this 10 problem test and get the best results from the test set:

**Before start,**go through the tutorials*Numbers, Number system and basic arithmetic operations***,**,*Factorizing or finding out factors*,*HCF and LCM**Basic concepts on fractions and decimals part 1,*or any other short but good material to refresh your concepts if you so require.*Ratio and proportion***Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 12 minutes.**When the time limit of 12 minutes is over,**mark up to which point you have answered,**but go on to complete the set.****At the end,**refer to the answers given in the end, to mark your score at 12 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

### 19th solution set—10 problems for SSC CGL Tier II exam: topic Profit and loss 2—Answering time 12 mins

**Problem 1.**

If the cost price is doubled and selling price is tripled, the profit would have become 65%. What is the present profit percentage?

- 10%
- 15%
- 20%
- 25%

**Solution 1: Problem analysis and solving in mind**

From given information profit is,

$3S-2C=0.65 \text{ of } 2C=1.3C$, where $S$ is the original selling price and $C$ the original cost price,

Or, $3S=3.3C$,

Or, $S=1.1C$.

Present profit is 10%.

Problem solved mentally using basic concepts. Just remember the rich concept of profit and loss—if profit is say 25%, sale price $S=C+0.25C=1.25C$, where $C$ is the cost price.

**Answer: **Option a: 10%.

**Key concepts used:** * Basic profit and loss concepts* --

*-- Correct variable selection as original variables*

**Rich profit and loss concepts**

**.****Problem 2.**

If a fruit-seller sells a coconut at Rs.14.4 he suffers 10% loss. If he wants to make a profit of 25%, then at what price should he sell?

- Rs.18
- Rs.16
- Rs.22
- Rs.20

**Solution 2: Problem analysis and solving in mind**

By given information and rich profit and loss concept,

$14.4=0.9C$, where $C$ is the cost price,

Or, $C=16$.

If target profit is 25%, the sale price would have to be,

$\text{Target sale price }=1.25\text{ of Cost price}$

$=\displaystyle\frac{5}{4}\times{16}$

$=20$.

**Answer:** Option d : Rs.20.

**Key concepts used:** Basic profit and loss concepts -- Rich profit and loss concept.

**Problem 3.**

The cost of 9 files, 6 notebooks, and 4 pens is Rs.305 while the cost of 2 files, 4 notebooks and 3 pens is Rs.145. What is the cost of 16 files, 8 notebooks and 5 pens?

- Rs.440
- Rs.415
- Rs.465
- Cannot be determined

**Solution 3: Problem analysis and solving in mind by key pattern identification**

This is not a problem on profit and loss. Nevertheless, it involves pure pattern identification which is the main objective of this test.

As such at first glance this problem does not seem to be solvable as there are three cost variables and two given equations.

But while solving these problems we always try to look for key patterns that will solve the problem in no time.

The key pattern is hidden here in the numbers of files, notebooks and pens of three expressions in relation to the first expression. If we sum up the three expressions we get,

$27F+18N+12P=450+x$, where $F$, $N$ and $P$ are the three costs of a file, a notebook and a pen respectively and $x$ is the desired target cost.

The LHS expression of this sum is exactly three times the first LHS expressions, that is,

$27F+18N+12P=3(9F+6N+4P)$,

Or, $450+x=915$,

Or, $x=465$.

**Answer:** c: Rs.465.

**Key concepts used:** *Key pattern identification in linear equation set***.**

With identification of the key pattern, the problem could easily be solved in mind.

**Problem 4. **

A fruit-seller buys bananas at 9 for Rs.8 and sells at 8 for Rs.9. What will be the profit or loss in percentage?

- 13.28% loss
- 13.28% profit
- 26.56% profit
- 26.56% loss

**Solution 4: Problem analysis and solving in mind**

More number of bananas are purchased at less price compared to sale situation. So it is sure that there is a profit.

To calculate the profit percentage we must first get the selling price of 9 bananas purchased.

8 bananas sold for $\text{Rs.9}$,

So 1 banana sold for $\text{Rs.}\displaystyle\frac{9}{8}$,

Finally at the third step of unitary method we get selling price of 9 bananas as,

$\text{Rs.}\displaystyle\frac{81}{8}$.

Profit is,

$\displaystyle\frac{81}{8}-8=\displaystyle\frac{17}{8}$.

Converting into percentage by dividing with cost price of Rs.8 and multiplying by 100,

$\text{Profit percentage}=\displaystyle\frac{\displaystyle\frac{17}{8}}{8}\times{100}$

$=\displaystyle\frac{17}{16}\times{25}$

$=25+\displaystyle\frac{25}{16}$.

At this point without calculating the exact percentage we can identify the answer as, option C, 26.56% profit as the last result clearly shows the profit to be more than 26%. This is efficient simplification along with free resource use of choice values.

**Answer:** Option c: 26.56% profit.

**Key concepts used:** Profit and loss basic concepts -- * efficient simplification* -- fraction arithmetic -- percentage concepts -- unitary method.

**Problem 5.**

If a pizza-seller sells a pizza at Rs.200, he suffers a 20% loss. If he wants to make a profit of 10%, then at what price should he sell a pizza?

- Rs.300
- Rs.250
- Rs.325
- Rs.275

**Solution 5: Problem analysis and solving in mind**

By first given information using rich concept of profit and loss as well as percentage concepts, first selling price is,

$200=0.8C$, where $C$ is the cost price.

So $C=250$.

For 10% profit on this cost price profit would be Rs.25, and selling price, Rs.275.

**Answer:** Option d: Rs.275.

**Key concept used:** Basic profit and loss concepts -- **Rich profit and loss concept -- percentage concepts.**

**Problem 6.**

Purchase cost of two watches were in ratio 16 : 23. If the cost of the first watch is increased by 10% and the second watch by Rs.477, the ratio changes to 11 : 20. The original purchase cost of the second watch is then,

- Rs.1696
- Rs.848
- Rs.932
- Rs.1219

**Solution 6: Problem analysis and solving in mind by pattern identification in the ratio**

Originally, $\displaystyle\frac{C_1}{C_2}=\frac{16}{23}$, where $C_1$ and $C_2$ are the costs of the first and second watch respectively.

The second watch cost then must be a multiple of 23. This is the key rule that results in the key pattern identification.

Among the choice values only the choice d: 1219 is a multiple of 23, and so it must be the solution.

#### Solution 6: Verification

Though in actual test environment we would never verify, for the benefit of your assurance, we are verifying the answer.

With $C_2=1219$, $C_1=16\times{53}=848$

So the second time,

$\displaystyle\frac{1.1C_1}{1219+477}=\displaystyle\frac{11}{20}$

Or, $\displaystyle\frac{0.1\times{848}}{1696}=\frac{1}{20}$.

The LHS also being $\displaystyle\frac{1}{20}$, the equation is satisfied.

This again is not a problem on profit and loss, but tests your pattern identification ability on ratio of cost figures.

**Answer:** Option d : Rs.1219.

**Key concepts used:** Basic ratio concepts -- Key pattern identification -- Factors multiples concept -- Free resource use of the choice values.

**Problem 7.**

When the cost price of an item increases by 25% what will be the new profit margin in percentage if the original profit were 150%?

- 25
- 50
- 75
- 100

**Solution 7: Problem analysis and solving in mind**

By the given information, and using rich profit and loss concept,

$S=2.5C_1$ where $S$ is the original sale price that remains unchanged and $C_1$ is the original cost price. 150% profit means sale price is 2.5 times cost price.

When cost price increases by 25%, new cost price,

$C_2=1.25C_1=\displaystyle\frac{1.25\times{S}}{2.5}$

Or, $S=\displaystyle\frac{2.5}{1.25}C_2=2C_2$.

Profit is 100% in new situation.

**Answer: **d: 100.

**Key concepts used:** Basic profit and loss concepts -- * Rich profit and loss concept* --

*Percentage concepts -- Event sequencing*

**.****Problem 8.**

A wholesale dealer sold some of his 200 dozens of mangoes at 20% profit and the rest at 10% profit, so that he made 13% profit on the two transactions taken together. How many mangoes (in dozens) did he sell at 20% profit?

- 80
- 140
- 120
- 60

**Solution 8: Problem analysis and solving in mind**

By given information,

$0.2N_1+0.1(200-N_1)=0.13\times(200)$, where $N_1$ is the number of dozens of mangoes sold at 20% profit,

Or, $0.1N_1=6$,

Or, $N_1=60$, the number of dozens sold at a profit of 20%.

For each of the three profit groups, per unit or per dozen profit is same, so that product of percentage profit of a group, say 20% profit group, and the number of units equals the actual profit made by selling that group.

**Answer:** Option d: 60.

**Key concepts used:** * Basic profit loss concepts* --

**Rich profit and loss concept -- Per unit profit concept -- Percentage concept.****Problem 9.**

The sale price of an item when sold at a profit of 8% is Rs.28 more than the sale price when it is sold at a loss of 8%. The cost price of the item is,

- Rs.175
- Rs.170
- Rs.190
- Rs.165

**Solution 9: Problem analysis and solving in mind**

As profit or loss percentages both are on the cost price, by the given statement, $8+8=16$% of cost price equals Rs.28. This is the difference between the two sale prices.

By unitary method, the 100% of cost price is then,

$C=\displaystyle\frac{28}{16}\times{100}=175$.

**Answer:** Option a: Rs.175.

**Key concepts used:** Basic profit and loss concepts -- Percentage reference concept -- Percentage concepts, the whole is 100% -- unitary method.

**Problem 10.**

The profit earned by selling an item for Rs.625 is same as the loss incurred if it is sold for Rs.545. The price at which it is to be sold for a gain of Rs.65 is then,

- Rs.630
- Rs.660
- Rs.650
- Rs.640

**Solution 10: Problem analysis and solving in mind**

By the given statement, the cost price is the average of the two sale prices, one on profit and the other at an amount of loss that is less than the cost price by the same amount as profit.

So cost price is,

$\displaystyle\frac{625+545}{2}=585$

For a profit of Rs.65, the sale price would then have to be that much more from the cost price, that is,

$585+65=650$.

**Answer:** c: Rs.650.

**Key concepts used:** Basic profit and loss concept -- Average equivalence of same profit and loss -- Same profit loss average cost -- Profit reference base as cost price.

Finally all the ten problems could be solved quickly in mind using basic and rich profit and loss concepts, percentage concepts and key pattern identification along with free resource use of choice values.

**Resources that should be useful for you**

* 7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests* or

*to access all the valuable student resources that we have created specifically for SSC CGL, but*

**section on SSC CGL****generally for any hard MCQ test.**

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#### How to solve difficult SSC CGL Math problems at very high speed using efficient problem solving strategies and techniques

These resources should be extremely useful for you to speed up your in-the-exam-hall SSC CGL math problem solving. You will find these under the subsection **Efficient Math Problem Solving.**

This is a collection of high power strategies and techniques for solving apparently tricky looking problems in various topic areas

usually within a minute.These are no bag of tricks but are based on concepts and strategies that are not to be memorized but to be understood and applied with ease along withpermanent skillset improvement.

**The following are the associated links,**

**How to solve SSC CGL level Profit and loss problems by Change analysis in a few steps 6**

**How to solve a difficult SSC CGL level Profit and Loss problem in a few steps 4**

**How to solve difficult SSC CGL Profit and loss problems in a few steps 3**

**How to solve similar problems in a few seconds, Profit and loss problem 2, Domain modeling**

**How to solve in a few steps, Profit and loss problem 1**