# Exercise : 4

^{2}= QR

(b) Q

^{2}= PR

(c) R

^{2}= PQ

(d) PQR = 100

(e) None of these

**Ans.b**

P = \(\frac{Q \times r \times t}{100}\) and Q = \(\frac{R \times r \times t}{100}\)

⇒ \(\frac{P}{Q} = \frac{Q}{R} = \frac{r \times t}{100}\)

∴ Q^{2} = PR.

(b) 8

(c) 9

(d) 7

(e) None of these

**Ans.b**

Interest for one year = 212.50 × ^{3}⁄_{100} × 1 = ^{51}⁄_{8}

Thus in 8 years, the interest is 51.

(b) 625

(c) 650

(d) 675

(e) None of these

**Ans.b**

Let he borrowed at 5% = x

∴ he borrowed at 7% = (2500 – x)

Now I_{1} + I_{2} = 275

⇒ 10x + 14(2500 – x) = 27500

⇒ 4x = 35000 – 27500 = 7500

⇒ x = Rs 1875

∴ Sum borrowed at 7% rate = 2500 – 1875 = 625

(b) 600 per year

(c) 700 per year

(d) 800 per year

(e) None of these

**Ans.c**

Shortcut method :

If borrowed amount be M and it is to be paid in equal instalments, then

\(M = na + \frac{ra}{100 \times Y} \times \frac{n\left(n - 1 \right)}{2}\)where Y = no. of instalments per annum

a = annual instalment

Here, M = 4200, y = 1, r = 10, n = 5, a = ?

4200 = 5a + ^{10a}⁄_{100} × ^{5(5 - 1)}⁄_{2}

⇒ 4200 = a[5 + 1] ⇒ 6a = 4200

⇒ a = 700

(b) 12,000

(c) 14,000

(d) 16,000

(e) None of these

**Ans.b**

Let the sum borrowed be x. Then,

\(\left(\frac{x \times 6 \times 2}{100} \right) + \left(\frac{x \times 9 \times 3}{100} \right) + \left(\frac{x \times 14 \times 4}{100} \right)\) = 11400⇒ (^{3}⁄_{25}x + ^{27}⁄_{100}x + ^{14}⁄_{25}x) = 11400 ⇒ ^{95}⁄_{100}x = 11400

⇒ x = \(\left(\frac{11400 \times 100}{95} \right)\) = 12000

Hence, sum borrowed = 12,000.

^{1}⁄

_{4}% p.a. for 2 years. Find his gain in the transaction per year.

(b) 125

(c) 150

(d) 167.50

(e) None of these

**Ans.a**

Gain in 2 years

= \(\left [ \left ( 5000 \times \frac{25}{4} \times \frac{2}{100} \right ) - \left ( \frac{5000 \times 4 \times 2}{100} \right )\right ]\)

= (625 – 400) = 225.

∴ Gain in 1 year = (^{225}⁄_{2}) = 112.50

(b) 245

(c) 350

(d) Cannot be determined

(e) None of these

**Ans.d**

We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.

(b) 1 : 4

(c) 2 : 3

(d) Data inadequate

(e) None of these

**Ans.c**

Let the principal be P and rate of interest be R%.

∴ Required Ratio = \(\left [ \frac{\left ( \frac{P \times R \times 6}{100} \right )}{\left ( \frac{P \times R \times 9}{100} \right )} \right ] = \frac{6PR}{9PR} = \frac{6}{9} = 2 : 3\)

(b) 600

(c) 750

(d) 900

(e) None of these

**Ans.d**

Difference of S.I. = \(\sqrt{31.50}\)

Let each sum be x. Then

\(\frac{x \times 4\tfrac{1}{2} \times 7}{100} - \frac{x \times 4 \times 7}{100} = 31.50\)or ^{7}⁄_{100}x × ^{1}⁄_{2} = ^{63}⁄_{2}

or x = 900

(b) 10,000

(c) 12,000

(d) Data inadequate

(e) None of these

**Ans.a**

Let the sum be x. Then,

\(\left ( \frac{x \times 6 \times 3}{100} \right ) + \left ( \frac{x \times 9 \times 5}{100} \right ) + \left ( \frac{x \times 13 \times 3}{100} \right ) = 8160\)⇒ 18x + 45x + 39x = (8160 × 100)

⇒ 102x = 816000

⇒ x = 8000.