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Maths MCQ

SimpleProfit and Loss · Maharashtra Board STD 7 (MSBSHSE - English Medium). 15 questions.

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15 questions · 14 auto-graded MCQ + 1 self-marked written.

MCQ 11 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a jug for $Rs. 144$, a man loses $\frac{1}{2}$ of his outlay. If it is sold for $Rs. 189$, what is the gain percent:
  • ✓
    $12.5\%$
  • B
    $25\%$
  • C
    $30\%$
  • D
    $50\%$
Answer
Correct option: A.
$12.5\%$

First $S.P.$ of jug $= Rs. 144$
Loss $=\frac{1}{7}$ of $C.P.$
Let $C.P. = x$
Then S.P $=\text{x}-\frac{1}{7}\text{x}$
$=\frac{6}{7}\text{x}$
$\therefore\frac{6}{7}\text{x}=144$
$\Rightarrow\text{x}=\frac{144\times6}{8}$
$=24\times7=\text{Rs. }168$
$\therefore C.P = Rs. 168$
Second $S.P. = Rs. 189$
Gain $= S.P. - C.P.$
$= 189 - 168 = Rs. 21$
$\text{Gain%}=\frac{\text{Gain}\times100}{\text{C.P}}$
$=\frac{21\times100}{168}=12.5\%$
Gain$\% = 12.5\%$

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MCQ 21 Mark
Mark $(\checkmark)$ against the correct answer in the following: A man buys a book for $Rs. 80$ and sells it for $Rs. 100$. His gain per cent is:
  • A
    $20\%$
  • ✓
    $25\%$
  • C
    $120\%$
  • D
    $125\%$
Answer
Correct option: B.
$25\%$
$C.P. = Rs. 80$
$S.P. = Rs. 100$
Gain $= S.P. - C.P. = Rs. 100 - 80 = Rs. 20$
$\therefore\text{Gain%}=\frac{\text{Gain}\times100}{\text{C.P}}$
$=\frac{20\times100}{80}$
$=25\%$
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MCQ 31 Mark
Mark $(\checkmark)$ against the correct answer in the following: A vendor bought lemons at $6$ for a rupee and sold them at $4$ for ampee. His gain$\%$ is:
  • ✓
    $50\%$
  • B
    $40\%$
  • C
    $33\frac{1}{3}\%$
  • D
    $16\frac{1}{3}\%$
Answer
Correct option: A.
$50\%$

$CP$ of $6$ lemons $=$ Re $1$
$CP$ of $1$ lemon $=\text{Rs. }\frac{1}{6}$
$CP$ of $4$ lemons $=$ Re $1$
$SP$ of $1$ lemon $=\text{Rs. }\frac{1}{4}$
$\therefore$ Gain $= SP - CP$
$=\frac{1}{4}-\frac{1}{6}$
$=\frac{3-2}{12}$
$=\text{Rs. }\frac{1}{12}$
Gain $= 10\%$
$\text{Gain%}=\frac{\text{Gain}\times100}{\text{C.P}}$
$=\frac{\frac{1}{12}\times100}{\frac{1}{6}}$
$=\frac{100\times6}{12}$
$=50\%$

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MCQ 41 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a stool for $Rs. 630$, a man loses $10\%$. The cost price of the chair is:
  • A
    $Rs. 567$
  • B
    $Rs. 693$
  • ✓
    $Rs. 700$
  • D
    $Rs. 730$
Answer
Correct option: C.
$Rs. 700$

$SP$ of stool $= Rs. 630$
Loss$\% = 10\%$
$\text{C.P.}=\frac{\text{S.P}\times100}{100-\text{loss%}}$
$=\frac{630\times100}{100-10}$
$=\text{Rs. }\frac{630\times100}{90}$
$=\text{Rs. }700$

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MCQ 51 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a pen for $Rs. 48$, a shopkeeper loses $20\%$. In order to gain $20\%$ what would be the selling price?
  • A
    $Rs. 52$
  • B
    $Rs. 56$
  • C
    $Rs. 68$
  • ✓
    $Rs. 72$
Answer
Correct option: D.
$Rs. 72$

First $S.P.$ of a pen $= Rs. 48$
Loss $= 20\%$
$\therefore\text{C.P.}=\frac{\text{S.P}\times100}{100-\text{loss%}}$
$=\frac{48\times100}{100-20}$
$=\frac{48\times100}{80}$
$= \text{Rs. } 60$
Gain $= 20\%$
Then $S.P.$ will be,
$=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{60\times(100+200)}{200}$
$=\frac{60\times120}{100}$
$= \text{Rs. } 72$

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MCQ 61 Mark
Mark $(\checkmark)$ against the correct answer in the following: If the cost price of $4$ toffees be equal to the selling price of $3$ toffees, then the gain$\%$is:
  • A
    $25\%$
  • B
    $30\%$
  • C
    $16\frac{2}{3}\%$
  • D
    $33\frac{1}{3}\%$
Answer

Let $CP$ of $4$ toffees $= SP$ of $3$ toffee $= Rs. 12$
$\text{(LCM}$ of $4, 3 = 12)$
$CP$ of $1$ toffee $=\text{Rs. }\frac{12}{4}=\text{Rs. }3$
$SP$ of $1$ toffee $=\text{Rs. }\frac{12}{3}=\text{Rs. }4$
Gain $= Rs. 4 - 3 = Rs. 1$
$\text{Gain%}=\frac{\text{Gain}\times100}{\text{C.P}}$
$=\frac{1\times100}{3}$
$=33\frac{1}{3}\%$

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MCQ 71 Mark
Mark $(\checkmark)$ against the correct answer in the following: If the cost price of $12$ pencils is equal to the selling price of $15$ pencils, then the loss per cent is:
  • ✓
    $20\%$
  • B
    $25\%$
  • C
    $3\%$
  • D
    $16\frac{2}{3}\%$
Answer
Correct option: A.
$20\%$

$C.P.$ of $12$ pencils
$= S.P$. of $15$ pencils
$= Re 1 ($suppose$)$
$\therefore C.P$ Of $1$ pencil $= \text{Rs. }\frac{1}{12}$
And $S.P$ of $1$ pencil $=\text{Rs. }\frac{1}{15}$
$\therefore$ Loss $= C.P - S.P$
$=\frac{1}{12}-\frac{1}{15}$
$=\frac{5-4}{60}$
$=\text{Rs. }\frac{1}{60}$
$\therefore\text{Loss%}=\frac{\text{Loss}\times100}{\text{C.P.}}$
$=\frac{\frac{1}{60}\times100}{\frac{1}{12}}$
$=\frac{1\times100\times12}{60\times1}$
$=20\%$

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MCQ 81 Mark
Mark $(\checkmark)$ against the correct answer in the following: If the cost price of $5$ bananas be equal to the selling price of $3$ bananas, then gain per cent is:
  • A
    $33\frac{1}{3}\%$
  • B
    $15\%$
  • ✓
    $66\frac{2}{3}\%$
  • D
    $40\%$
Answer
Correct option: C.
$66\frac{2}{3}\%$

Let the cost price of each banana be $Rs. 1$
Cost price of three bananas $= Rs. 3$
$SP$ of three bananas $= CP$ of five bananas$ = Rs. 5$
Gain $= SP - CP = Rs. (5 - 3) = Rs. 2$
$\text{Gain%}=\Big(\frac{\text{Gain}}{\text{C.P.}}\times100\Big)\%$
$=\Big(\frac{2}{3}\times100\Big)\%$
$=\Big(\frac{200}{3}\Big)\%$
$=66\frac{2}{3}\%$

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MCQ 91 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a bat for $Rs. 100$, a man gains $Rs. 20$ His gain per cent is:
  • A
    $20\%$
  • ✓
    $25\%$
  • C
    $18\%$
  • D
    $22\%$
Answer
Correct option: B.
$25\%$

$S.P. = Rs. 100$
Gain $= Rs. 20$
$C.P. = S.P. -$ gain $= Rs. 100 - 20 = Rs. 80$
$\text{Gain%}=\frac{\text{Gain}\times100}{\text{C.P}}$
$=\frac{20\times100}{80}$
$=25\%$

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MCQ 101 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling an article for $Rs. 144$ a man loses $10\%$. At what price should he sell it to gain $10\%?$
  • A
    $Rs. 158.40$
  • B
    $Rs. 158.40$
  • ✓
    $Rs. 176$
  • D
    $Rs. 192$
Answer
Correct option: C.
$Rs. 176$
$SP$ of an article $= Rs. 144$
Loss$\% = 10\%$
$\therefore\text{C.P.}=\frac{\text{S.P}\times100}{100-\text{loss%}}$
$=\frac{144\times100}{100-10}$
$=\frac{144\times100}{90}$
$=\text{Rs. }160$
Gain $= 10\%$
$\text{SP}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{160(1400+10)}{100}$
$=\text{Rs. }\frac{160\times110}{100}$
$=\text{Rs. }176$
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MCQ 111 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a jug for $Rs. 168$, a man loses $\frac{1}{7}$ of his outlay. The cost price of the jug is:
  • A
    $Rs. 144$
  • B
    $Rs. 192$
  • ✓
    $Rs. 196$
  • D
    None of these.
Answer
Correct option: C.
$Rs. 196$

Let the cost price of the jug be $Rs. x$
$\text{Loss}=\text{Rs. }\frac{\text{x}}{7}$
$SP$ of the jug $= CP -$ Loss
$=\text{Rs. }\Big(\text{x}-\frac{\text{x}}{7}\Big) $
$=\text{Rs. }\frac{6}{7}\text{x}$
$SP$ of the jug $= Rs. 168 ($given$)$
$\therefore\frac{6}{7}\text{x}=168$
$\Rightarrow\frac{168\times7}{6}$
$\Rightarrow\text{x}=\frac{1176}{6}$
$\Rightarrow\text{x}=196$
$CP$ of the jug,
$= Rs. 196$

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MCQ 121 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a football for $Rs. 100$, a man gains $Rs. 15$. The cost price of the football is:
  • A
    $Rs. 115$
  • ✓
    $Rs. 85$
  • C
    $Rs. 70$
  • D
    $Rs. 130$
Answer
Correct option: B.
$Rs. 85$

$SP$ of a football $= Rs. 100$
Gain $= Rs. 15$
Gain $= SP - CP$
$\Rightarrow 15 = 100 - CP$
$\Rightarrow CP = Rs. (100 - 15)$
$\Rightarrow CP = Rs. 85$

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MCQ 131 Mark
Mark $(\checkmark)$ against the correct answer in the following: On selling a racket for $Rs. 198,$ a shopkeeper gains $10\%$. The cost price of the racket is:
  • ✓
    $Rs. 180$
  • B
    $Rs. 178.20$
  • C
    $Rs. 217.80$
  • D
    $Rs. 212.50$
Answer
Correct option: A.
$Rs. 180$

$S.P. = Rs. 198$
Gain $= 10\%$
$\therefore\text{C.P.}=\frac{\text{S.P}\times100}{100+\text{gain%}}$
$=\frac{198\times100}{100+10}$
$=\frac{198\times100}{110}$
$=\text{Rs. }180$

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MCQ 141 Mark
Mark $(\checkmark)$ against the correct answer in the following: A football is bought for $Rs. 120$ and sold for $Rs. 105$. The loss is:
  • ✓
    $12\frac{1}{2}\%$
  • B
    $14\frac27\%$
  • C
    $16\frac23\%$
  • D
    $13\frac13\%$
Answer
Correct option: A.
$12\frac{1}{2}\%$
$C.P. = Rs. 120$
$S.P. = Rs. 105$
Loss $= C.P. - S.P. = Rs. 120 - 105 = Rs. 15$
$\therefore\text{Loss}\%=\frac{15\times100}{120}$
$=\frac{25}{2}\%$
$=12\frac12\%$
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MCQ 151 Mark
Mark $(\checkmark)$ against the correct answer in the following: A vendor buys lemons at $Rs. 25$ per dozen and sells at $5$ for $Rs. 12$. His gain per cent is:
  • A
    $14.5\%$
  • B
    $15\%$
  • ✓
    $15.2\%$
  • D
    $16\%$
Answer
Correct option: C.
$15.2\%$

Cost price of $12$ bananas $= Rs. 25$
Cost price of one banana $=\text{Rs. }\frac{25}{12}$
Cost price of five bananas $=5\times\frac{25}{12}$
$=\frac{125}{12}=10.42$
He shells five bananas at the cost $(SP) $of $Rs. 12.$
Gain $= SP - CP = Rs. (12 - 10.42) = Rs. 1.58$
$\text{Gain%}=\Big(\frac{\text{Gain}}{\text{C.P.}}\times100\Big)\%$
$=\Big(\frac{1.58}{10.4}\times100\Big)\%$
$=15.2\%$

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