search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
1 vote
59 views

A shop owner bought a total of $64$ shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was $\text{INR} \; 50$ less than that of a large shirt. She paid a total of $\text{INR} \; 5000$ for the large shirts, and a total of $\text{INR} \; 1800$ for the small shirts. Then, the price of a large shirt and a small shirt together, in $\text{INR},$ is 

  1. $200$
  2. $175$
  3. $150$
  4. $225$
in Quantitative Aptitude 2.7k points 5 79 342
retagged by
59 views

1 Answer

1 vote
Let the number of large shirts is $l$ and the number of small shirts is $s.$

$\boxed{s+l=64}$

Let the price of a small shirt be $p,$ and then the price of a large shirt be $p+50.$

Money she spent on small shirts $= \text{sp} = 1800 \; \longrightarrow (1)$

Money she spent on large shirts $= l(p+50) = 5000$

$\Rightarrow (64-s)(p+50) = 5000$

$\Rightarrow 64p + 3200 – \text{sp} – 50s = 5000$

$\Rightarrow 64p – 50s – 1800 = 1800$

$\Rightarrow 64p – 50s = 3600$

$\Rightarrow 32p – 25s = 1800$

$\Rightarrow 32p – 25\left(\frac{1800}{p}\right) = 1800$

$\Rightarrow 32p^{2} – 45000 = 1800p$

$\Rightarrow 32p^{2} – 1800p – 45000 = 0$

$\Rightarrow 4p^{2} – 225p – 5625 = 0$

$\Rightarrow p = \frac{-(-225) \pm \sqrt{(-225)^{2} – 4(4)(-5625)}}{2(4)}$

$\Rightarrow p = \frac{225 \pm \sqrt{50625+90000}}{8}$

$\Rightarrow p = \frac{225 \pm \sqrt{140625}}{8}$

$\Rightarrow p = \frac{225 \pm 375}{8}$

$\Rightarrow p = \frac{225+375}{8}, \; \frac{225-375}{8}$

$\Rightarrow p = \frac{600}{8}, \; \frac{-150}{8}$

$\Rightarrow \boxed{p=75, \; {\color{Red} {\frac{-75}{4} \;\text{(rejected)}}}}$

The price of small shirt $ = p = ₹ 75.$

The price of large shirt $ = p+50 = 75+50= ₹ 125.$

$\therefore$ The price of a large shirt and a small shirt together, in INR $= 75+125 =₹ 200.$

Correct Answer $:\text{A}$
10.1k points 4 8 30
edited by
Answer:

Related questions

1 vote
1 answer
1
46 views
If $n$ is a positive integer such that $( \sqrt[7]{10}) ( \sqrt[7]{10})^{2} \dots ( \sqrt[7]{10})^{n} > 999,$ then the smallest value of $n$ is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 46 views
1 vote
1 answer
2
66 views
Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, \dots $ such that $x_{n+1} = x_{n} + n – 1$ for all $n \geq 1.$ If $x_{1} = -1$ then $x_{100}$ is equal to $4950$ $4850$ $4849$ $4949$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 66 views
1 vote
1 answer
3
131 views
Anil can paint a house in $12 \; \text{days}$ while Barun can paint it in $16 \; \text{days}.$ Anil, Barun, and Chandu undertake to paint the house for $ ₹ \; 24000$ and the three of them together complete the painting in $6 \; \text{days}.$ If Chandu is paid in proportion to the work done by him, then the amount in $\text{INR}$ received by him is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 131 views
1 vote
1 answer
4
67 views
For a real number $a,$ if $\dfrac{\log_{15}a + \log_{32}a}{(\log_{15}a)(\log_{32}a)} = 4$ then $a$ must lie in the range $a>5$ $3<a<4$ $4<a<5$ $2<a<3$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 67 views
1 vote
1 answer
5
78 views
In a triangle $\text{ABC}, \angle \text{BCA} = 50^{\circ}. \text{D}$ and $\text{E}$ are points on $\text{AB}$ and $\text{AC},$ respectively, such that $\text{AD = DE}.$ If $\text{F}$ is a point on $\text{BC}$ such that $\text{BD = DF},$ then $\angle \text{FDE, in degrees},$ is equal to $96$ $72$ $80$ $100$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 78 views
...