# 100+ Chain rule problems for Bank exams - 1

Question: 1

12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required is

(A) 4

(B) 8

(C) 12

(D) 16

Ans: B

Let the required number of men be x.

Less days, More men (Indirect Proportion)

More working hrs per day,

Less men (Indirect Proportion)

Days | 8 : 10 | |

: : 12 : x | ||

Working Hrs | 15 : 8 |

∴ 8 × 15 × x = 10 × 8 × 12

⇔ x = ${10 × 8 × 12}/{8 × 15}$ ⇔ x = 8.

Question: 2

If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?

(A) Rs. (xd)

(B) Rs. (yd)

(C) $$Rs. ({yd}/{x})$$

(D) $$Rs. ({xy}/{d})$$

Ans: C

Cost of x metres = Rs.d.

Cost of 1 metre = Rs.($d/x$).

Cost of y metres = Rs.($d/x$ × y) = Rs.(${yd}/x$).

Question: 3

30 labourers, working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers to finish the same piece of work in 30 days, will be

(A) 15

(B) 18

(C) 21

(D) 24

Ans: C

Let the required number of labourers be x. Then,

Less working hrs/day, More labourers (Indirect Proportion)

More days, Less labourers (Indirect Proportion)

Working Hrs/Day | 6 : 7 | |

: : 30 : x | ||

Days | 30 : 18 |

∴ 6 × 30 × x = 7 × 18 × 30 ⇔ 6x = 126 ⇔ x = 21.

Question: 4

20 men complete one third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days?

(A) 10

(B) 11

(C) 12

(D) 14

Ans: C

Let the total number of men be x.

Work done = $1/3$, Remaining work = $(1 – 1/3) = 2/3$

More work, More men (Direct Proportion)

More days, Less men (Indirect Proportion)

Work | $1/3 : 2/3$ | |

: : 20 : x | ||

Days | 25 : 20 |

∴ $(1/3 × 25 × x) = (2/3 × 20 × 20) ⇔ x = 800/25 = 32.$

∴ More men to be employed = (32 – 20) = 12.

Question: 5

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

(A) 10

(B) 12

(C) 14

(D) 16

Ans: B

Let the required number of working hours per day be x.

More pumps,

Less working hours per day (Indirect Proportion)

Less days,

More working hours per day (Indirect Proportion)

Pumps | 4 : 3 | |

: : 8 : x | ||

Days | 1 : 2 |

∴ 4 × 1 × x = 3 × 2 × 8

⇔ x = ${3 × 2 × 8}/4$ ⇔ x = 12.

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